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Deb normally drives to work in 45 minutes at an average speed of 40 miles per hour. This week, however, she plans to bike to work along a route that decreases the total distance she usually travels when driving by 20% . If Deb averages between 12 and 16 miles per hour when biking, how many minutes earlier will she need to leave in the morning in order to ensure she arrives at work at the same time as when she drives?
- a)135
- b)105
- c)95
- d)75
- e)45
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Deb normally drives to work in 45 minutes at an average speed of 40 mi...
This standard rate problem will rely heavily on the formula RT=D, where R is the rate, T is the time and D is the distance traveled.
First, we should find the driving and biking distances:
If Deb drives for 45 minutes, or 0.75 hours, at a rate of 40mph, she drives a total distance of
(0.75)(40) = 30 miles.
If the bike route is 20% shorter than the driving route, the bike route is 30 – 30(0.2) = 30 – 6 = 24 miles.
Next, we need to determine how long it will take Deb to travel the route by bike. She wants to ensure that she'll get to work by a particular time, so we want to calculate the longest possible time it could take her; therefore, we have to assume she will bike at the slowest end of the range of the speeds given: 12mph. If she travels 24 miles at 12mph, it will take her 24/12 = 2 hours or 120 minutes.
If Deb normally takes 45 minutes to drive to work but could take up to 120 minutes to bike to work, then she must leave 120 – 45 = 75 minutes earlier than she normally does to ensure that she will arrive at work at the same time.
The correct answer is D.
First, we should find the driving and biking distances:
If Deb drives for 45 minutes, or 0.75 hours, at a rate of 40mph, she drives a total distance of
(0.75)(40) = 30 miles.
If the bike route is 20% shorter than the driving route, the bike route is 30 – 30(0.2) = 30 – 6 = 24 miles.
Next, we need to determine how long it will take Deb to travel the route by bike. She wants to ensure that she'll get to work by a particular time, so we want to calculate the longest possible time it could take her; therefore, we have to assume she will bike at the slowest end of the range of the speeds given: 12mph. If she travels 24 miles at 12mph, it will take her 24/12 = 2 hours or 120 minutes.
If Deb normally takes 45 minutes to drive to work but could take up to 120 minutes to bike to work, then she must leave 120 – 45 = 75 minutes earlier than she normally does to ensure that she will arrive at work at the same time.
The correct answer is D.
Most Upvoted Answer
Deb normally drives to work in 45 minutes at an average speed of 40 mi...
To determine how many minutes earlier Deb needs to leave in the morning, we need to calculate the difference in time it takes her to travel to work when driving and when biking.
1. Calculate the distance Deb usually travels when driving:
- Deb drives at an average speed of 40 miles per hour for 45 minutes.
- Distance = Speed * Time = 40 miles/hour * 45 minutes = 30 miles.
2. Calculate the reduced distance when biking:
- The total distance is decreased by 20% (or 0.2).
- Reduced distance = 30 miles - (0.2 * 30 miles) = 30 miles - 6 miles = 24 miles.
3. Determine the range of possible speeds when biking:
- Deb averages between 12 and 16 miles per hour when biking.
4. Calculate the time it takes to bike to work at the lower speed:
- Time = Distance / Speed = 24 miles / 12 miles per hour = 2 hours.
5. Calculate the time it takes to bike to work at the higher speed:
- Time = Distance / Speed = 24 miles / 16 miles per hour = 1.5 hours.
6. Calculate the difference in time between biking and driving:
- Time difference = Time - 45 minutes.
- For the lower speed: Time difference = 2 hours - 45 minutes = 1 hour and 15 minutes.
- For the higher speed: Time difference = 1.5 hours - 45 minutes = 45 minutes.
7. Determine the maximum time difference:
- Deb needs to leave early enough to account for the maximum time difference, which is 1 hour and 15 minutes.
8. Convert the time difference to minutes:
- 1 hour and 15 minutes = 60 minutes + 15 minutes = 75 minutes.
Therefore, Deb needs to leave 75 minutes earlier in the morning to ensure she arrives at work at the same time as when she drives. The correct answer is option D.
1. Calculate the distance Deb usually travels when driving:
- Deb drives at an average speed of 40 miles per hour for 45 minutes.
- Distance = Speed * Time = 40 miles/hour * 45 minutes = 30 miles.
2. Calculate the reduced distance when biking:
- The total distance is decreased by 20% (or 0.2).
- Reduced distance = 30 miles - (0.2 * 30 miles) = 30 miles - 6 miles = 24 miles.
3. Determine the range of possible speeds when biking:
- Deb averages between 12 and 16 miles per hour when biking.
4. Calculate the time it takes to bike to work at the lower speed:
- Time = Distance / Speed = 24 miles / 12 miles per hour = 2 hours.
5. Calculate the time it takes to bike to work at the higher speed:
- Time = Distance / Speed = 24 miles / 16 miles per hour = 1.5 hours.
6. Calculate the difference in time between biking and driving:
- Time difference = Time - 45 minutes.
- For the lower speed: Time difference = 2 hours - 45 minutes = 1 hour and 15 minutes.
- For the higher speed: Time difference = 1.5 hours - 45 minutes = 45 minutes.
7. Determine the maximum time difference:
- Deb needs to leave early enough to account for the maximum time difference, which is 1 hour and 15 minutes.
8. Convert the time difference to minutes:
- 1 hour and 15 minutes = 60 minutes + 15 minutes = 75 minutes.
Therefore, Deb needs to leave 75 minutes earlier in the morning to ensure she arrives at work at the same time as when she drives. The correct answer is option D.
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