## Wednesday, July 09, 2014

### Time Speed & Distance Level 2 Question Solving - 10 July 2014

Question Number 1 - Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?

Answer - Suppose at a speed of 10 km/hr he takes (x +2) hours to cover the distance then according to the condition given in the question at a speed of 15 km/hr he would take x hours to cover the distance.

Distance travelled by both of them is constant so -  10(x +2) = 15x

Solving we get, x = 4 hours.

Distance to be travelled is 10(x +2) = 15(x) = 15 * 4 = 60 km.

So we get to know that both of them started there journey at 8:00 am in the morning.

So reach at 1 P.M. 5 hours time is available.

So the speed to reach at 1 P.M. would be -  60 km/5 = 12 km/hr

12 km/hr

Question Number 2 - A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?

Answer - Speed in m/sec = 600/300 = 2 metre/second

In order to change metre/second in Km per hour multiply by 18/5.

2 * 18/5 = 7.2 km/h

7.2 km/h

Question Number 3 - If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:

Answer - Suppose for the time he travelled is x hours.

Then 14 x - 10 x = 20

4 x = 20

x = 5 hours.

Actual Distance = 10 x = 50 km.

50 km

Question Number 4 - A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:

Answer - Let the speed of the car be s km/hr then the speed of the train would be 1.5 s km/hr

Both are covering the same distance with the only difference that the train is taking 12.5 minutes than car to travel the same distance so the equation would be something like this -

1.5 s * (t - 12.5/60) = s * t

t = 5/8 hours

So the speed of the car would be = Distance/Time Taken = 75/(5/8) = 120 km/hr

The Speed of the Car is 120 km/hr

Question Number 5 - Excluding stoppages, the speed of a bus is 54 km/h and including stoppages, it is 45 km/h. For how many minutes does the bus stop per hour?

Answer - Moving constantly in 60 minutes distance travelled in 54 km. But including stoppages in 60 minutes he is covering 45 km. So due to stoppages he covered 9 km less. So for covering 9 km at original speed of 54 km/h it would take (9/54 * 60) = 10 minutes.

So considering stoppages the bus stops for 10 minutes every hour.

10 minutes

Question Number 6 - In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:

Answer - Let the original time taken be t hours.

So, 600 t = 400 (t + 1/2)

t = 1 hours

Duration of the flight is 1 hour

Question Number 7 - A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

Answer - For first 5 hours at the rate of 21 km/hr. So distance travelled = 21*5 = 105 km

For first 5 hours at the rate of 24 km/hr. So distance travelled = 24*5 = 120 km

So total distance travelled = 105 + 120 = 225 km

Question Number 8 - The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:

Answer - Speed of the second train is = 400/4 = 100 km/hr

Ratio of speeds = 7:8

So suppose the original speeds of first and second train - 7x and 8x

8x = 100, So 7x = 87.5 km/hr

Speed of first train = 87.5 km/hr

Question Number 9 - A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:

Answer - Time taken to cover first 160 km = 160/64 hours.

Time taken to cover second 160 km = 160/80 = 2 hours.

Total time taken = 2 + 2.5 = 4.5 hours.

Total distance travelled = 320/4.5 = 71.11 km/hr

71.11 km/hr

Question Number 10 - A car travelling with  of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the car.

Answer 1 hr 40 min 48 sec = 1 + 40/60 + 48/3600 = 126/75 hours.

Distance Travelled = 42 km

Actual Speed = 42 / (126/75) = 25 km/hr.

1. Sir I have a doubt from TSD. Please clear it. The question is as follows:

There are 2 buses which shuttle between a hill station at the top of a hill and a town at the bottom of the hill. They both start at the same time - one from the bottom and the other from the top of the hill. They both travel along the same route and cross each other at a certain point. After they cross, 8 times the time taken by the bus going downhill is equal to the difference between the time taken by the two buses to reach their destinations from their meeting point.

1. The difference between the times taken by them to reach their respective destinations from their meeting point is 16 hours. How many hours after their start do they meet?

2. The speed of the bus from the bottom of hill to the top is 10 kmph and it takes 8 hrs more than the bus from the top to compete its trip. What is the distance between the top and the bottom of the hill?

2. Resting 9 hrs a day a man travels a certain distance in 40days. resting double the time how many days will he take double the distance at double the speed?