Test: Speed, Time and Distance - 2 - UCAT MCQ

To find the speed of the train, we first need to find the speed of the steamer and the speed of the horse transit. The total distance traveled is 120 km + 450 km + 60 km = 630 km, and the total time taken for the journey is 13.5 hours. Therefore, the average speed of the journey is 630 km / 13.5 hours = 46.67 km/hr.

Since the speed of the train is three times that of the horse-transit and 1.5 times that of the steamer, we can write the following equations:

t = 3h t = 1.5s

where t is the speed of the train, h is the speed of the horse transit, and s is the speed of the steamer. Solving these equations, we find that the speed of the horse transit is 23.01 km/hr and the speed of the train is 69.03 km/hr.

Therefore, the speed of the train is 69.03 km/hr. The correct answer is B

Lalloo is unfortunate that the friend is moving away from him.

(Because the friend moves in same direction as Lalloo).

relative speed= 20- 15= 5,kmph. distance= 200 m.

Thus, Lalloo will meet his friend when he gains 200 m over him.

⇒ time required = distance / speed = 0.2/5 = 1/25 hrs.

⇒ Distance travelled by the friend in 1/25 hrs. (when Lalloo catches up him)

⇒ Time x Speed = 1/25 x 15 = 3/5 km = 600 m

The answer is 5.8 km.

Let the distance to the station be x km.

Time taken to reach the station at 5 kmph = x/5 hours.

Time taken to reach the station at 7 kmph = x/7 hours.

Given that the time taken to reach the station at 5 kmph is 10 minutes more than the time taken to reach the station at 7 kmph.

Therefore, x/5 - x/7 = 10/60

Solving for x, we get x = 5.8.

Hence, the distance to the station is 5.8 km.

The distance travelled is 7.5 km.

Let the time taken by the athlete travelling at 10 kmph be t hours.

The time taken by the athlete travelling at 15 kmph is t+15/60 hours.

The distance travelled by both athletes is the same.

Therefore, 10t = 15(t+15/60)

Solving for t, we get t = 3/4 hours.

The distance travelled by both athletes is 10t = 10 x 3/4 = 7.5 km.

The original speed of the jeep is 20 kmph.

Let the original speed of the jeep be x kmph.

Time taken to cover 100 km at original speed = 100/x hours.

Time taken to cover 100 km at increased speed = 100/(x + 5) hours.

Given that the time taken to cover 100 km at increased speed is 1 hour less than the time taken to cover 100 km at original speed.

Therefore, 100/x - 100/(x + 5) = 1

Solving for x, we get x = 20.

Hence, the original speed of the jeep is 20 kmph.

It is given in the question that a man crosses 600m long street in 5 minutes. We have to find the speed of the man in km per hour. To find the speed of the man in km per hour, we have to convert the given distance to km and also convert the given time to hour.
First, let us see the conversion of the given distance into km. We know that 1km = 1000m.
So, to convert 600m to km, we can write, 600m = x km.
x = 600/1000 km 
x = 0.6km 
Now, let us convert the given time into hours. We know that 1 hour = 60 minutes.
So, to convert 5 minutes to hours, we can write, 5 minutes = y hours.
y = 5/60 hrs
y = 0.083 hrs
Now we know that speed can be found out using the formula, Speed=Distance/Time, We have found out that distance = 0.6km and time = 0.083 hrs. So, on substituting these values in the formula of speed, we get,  
Speed = 0.6/ 0.083
= 6 × 1000 / 83 × 10
= 6000/ 830
= 600/83
= 7.2 km/h
Therefore, we get the speed of the man crossing a 600m long street in 5 minutes as 7.2km/h.
Hence, option (D) is the correct answer.

Let the distance be x km. Then,
(Time taken to walls x km) + (Time taken to ride x km) = 23/4 hrs
⇒  (Time taken to walls 2x km) + Time taken to ride 2x km  =  23/2 hrs
but time taken to ride 2x km = 15/4 hrs 
Therefore, Time taken to walk 2x km = (23/2 - 15/4) hrs = 31/4 hrs =7 hr 45 min.

It is given that, excluding stoppages, the speed of a bus is 54 kmph.
⇒ Distance travelled by bus in 1 hour, excluding stoppages = 54 km.
Also, it is given that including stoppages the speed of the bus is 45 km/hr.
⇒ Distance travelled by the bus in 1 hour, including stoppages = 45 km.
(Distance travelled by bus in 1 hour excluding stoppages – distance travelled by bus in 1 hour including stoppages)
⇒ (54km − 45km) ⇒ 9 km
Due to stoppages, it covers 9 km less in an hour.
Students can easily solve this question by using this trick.
Required time for the stoppage per hour,

Let time taken to travel the first half = x hr 
⇒ Time taken to travel the second half = (10 - x) hr 

∵ Distance = Time * Speed
Distance covered in the first half = 21x 
Distance covered in the the second half = 24(10 - x)

∵  Distance covered in the the first half = Distance covered in the the second half
⇒ 21x = 24(10 - x)
⇒ 45x = 240
⇒ x = 16/3

Total Distance = 2 x 21(16/3) = 224 Km [∵ multiplied by 2 as 21x was the distance of half way]

Time taken = 1 hr 40 min 48 sec = 1 hr (40 + 4/5) min = 1 + 51/75 hrs = 126/75 hrs
Let the actual speed be x km/hr
Then, (5/7) * x * (126/75) = 42
⇒ x = 42 x 7 x (75 / 5) x 126
⇒ x = 35 km/hr