Alice, while driving to her workplace completes an initial distance of 50 miles in 2 hours and remaining 60 miles in 3 hours. What is the average speed in miles per hour for her entire journey?
Average speed :
Total distance / Total time
⇒ (50+60) miles / (2+3) hours
⇒ 110/ 5
⇒ 22 miles / hour
Alice travels at an average speed of 60miles per hour from her home to a grocery store. She travels back to her home via same route at an average speed of 80 miles per hour. What is the average speed of her entire journey?
Alan starts his journey from point A at sharp 10.00am. He drives at an average speed of 30 miles per hour and reaches Point B at 11.00 am. Bob starts his journey 15 mins after Alan started his journey and travels via same route as Alan did. If Alan and Bob both reached point B exactly at the same time, then what is Bob’s average speed (in miles per hour)?
A speed boat travels at a speed of x miles per hour in still water. With a favourable current, the speed boat travels downstream and reaches its destination in 2.5 hours. The speedboat travels back upstream against the current and covers the same distance in 3.5 hours. If the speed of the current is 1mph, then what is the value of x?
During a trip, Charles covered the first part of a certain distance at an average speed of 30 miles per hour and the remaining part at an average speed of 50 miles per hour. If the ratio of time taken to cover the first part and remaining part is 2: 3, then what is the total distance that Charles travelled?
(1) It took a total of 5 hours to complete the entire distance.
(2) 2/7^{th} of the entire distance was covered during the first part
Two dogs are running towards each other from opposite ends of a twomile track. Dog 1 has a speed of 12 mph and Dog 2 has a speed of 8 mph. How many miles from Dog 1’s starting position will they meet?
Step 1: Question statement and Inferences
Let the two dogs meet at a distance of x miles from the Starting position of Dog 1.
So, Dog 1 covers a distance of x miles at a speed of 12 mph to reach the meeting point.
In the same time, Dog 2 covers a distance of (2x) miles at a speed of 8 mph to reach the meeting point
Step 2: Finding required values
We know that
Since the time taken by Dog 1 to reach the meeting point is equal to the time taken by Dog 2 to reach the meeting point, we can write:
The dogs will meet 6/5 miles from Dog 1’s starting position.
Answer: Option (B)
Riding her bicycle downhill, Sam reached the bottom of the 10mile trail 10 minutes faster than it took her, riding 12 miles per hour, to reach the top of the trail. What was her downhill speed?
Step 1: Question statement and Inferences
Riding 10 miles at her new speed took Sam 10 minutes less than riding the same distance at 12 miles per hour. What was this new speed?
Step 2: Finding required values
Start by finding the time it took Sam to reach the top of the hill.
Her uphill speed, u = 12 miles per hour
Distance travelled = 10 miles
Now considering the downhill journey,
Step 3: Calculating the final answer
Answer: Option (B)
Johnny drove with an average speed of m miles per hour for h hours, increased his average speed to m + s miles per hour for an additional h hour and then increased his average speed to twice the original speed for a final h hours. Which of the following represents the distance which he drove?
Step 1: Question statement and Inferences
Johnny drove three segments for h hours each. His speeds were m, m + s, and 2m. The question asks for the representation of the distance which he drove.
We know that
Step 2: Finding required values
Multiply the time driven, h for each segment, by the speed driven for that segment, to get distances. These are hm, h(m + s), and 2hm, respectively.
Step 3: Calculating the final answer
The total distance traveled is hm + h(m + s) + 2hm, which factors out to h(4m +s).
Answer: Option (B)
Emily rode x miles from her home at a speed of p miles per hour before running out of fuel. She then walked her motorcycle at 8 meters per minute till a few miles further before she met her friend. Emily’s friend dropped her back home, driving along the same route at a rate that was 50% greater than Emily’s riding speed for x miles. If the total journey took t hours, how many miles did Emily walk her motorcycle for? (Given : 1000 meters = 0.62 miles)
Given:
Let’s call Emily’s journey from her home till she meets her friend as her “Forward Journey” and her journey from when she meets her friend till her home as her “Return Journey”
Forward Journey
Return Journey
So our DST table would look like this:
*(t_{1 }+ t_{2 }+ t_{3}) = t hours
To Find: How many miles she has walked her motorcycle = y = ?
Linkages
Approach
Calculation
2. From home to “Ran out of fuel” point row of the DST table, we will get t1 in terms of x and p.
3. From “Emily “meets her friend” to home row of the DST table, we will get t2 in terms of y.
4. (t_{1 }+ t_{2 }+ t_{3}) = t hours
To get rid of the decimal in the denominator multiply both sides of the equation by 1/10
Correct Answer: Option D
To reach her office from her home, Karen traveled x miles at a speed of y miles per hour. On her way back, via the same route, she travels for ten miles before stopping for an hour. If Karen drove at y miles per hour till she stopped, by what percentage should she increase her speed so that the overall time taken to reach back home from the office is the same as that taken to reach the office from home?
Jonathan drove from City A to City B at a rate of 1.2 minutes per kilometer. He then drove back to City A from City B , along the same route, at 1 minute per kilometer. If he took anywhere between 3 hours to 5 hours to travel from City A to City B and between 2 hours to 3 hours on his way back, what could be the distance between the two cities?
Phil drives east from his home for 2 hours before realizing that he will run out of fuel in another 70 miles. Nevertheless, he drives for another 10 miles east before returning back home via the same route. If he drives at a constant speed throughout his journey and returns home with fuel left for another 10 miles, how much time does he take for his journey eastwards?
Every day, Tom walks from his home to his office, via the same route, covering s feet at a speed of x feet per minute. Today he took a different route and ended up walking 10% more than he usually does, at a speed that was 100 meters per minute faster than his usual speed. What is the percentage change in the time he took today compared to the time he takes on a usual day? (1 feet =0.3 meter)
A train takes two hours to travel from one station to the other. What is the distance between the two stations?
(1) The train covers one third of the total distance in the first hour at an average speed of 80 mph.
(2) The average speed during the second hour is 160 mph.
A man rows at the rate of 5 mph in still water. If the river runs at the rate of 1 mph, it takes him 1 hour to row to a place and come back. What is the total distance covered by him in miles?
Correct Answer : e
Explanation : Speed downstream = (5 + 1) kmph = 6 mph.
Speed upstream = (5  1) kmph = 4 mph.
Let the required distance be x m.
Then, x/6 + x/4 = 1
2x + 3x = 12
5x = 12
x = 2.4 m.
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