Advertisements
Advertisements
Question
The distance by road between two towns A and B is 216 km and by rail it is 208 km. A car travels at a speed of x km/hr and the train travels at a speed which is 16 km/hr faster than the car. Calculate:
- the time taken by the car to reach town B from A, in terms of x;
- the time taken by the train to reach town B from A, in terms of x.
- If the train takes 2 hours less than the car, to reach town B, obtain an equation in x and solve it.
- Hence, find the speed of the train.
Advertisements
Solution
Speed of car = x km/hr
Speed of train = (x + 16) km/hr
i. We know: Time = `"Distance"/"Speed"`
Time taken by the car to reach town B From A = `216/x` hrs
ii. Time taken by the train to reach town B from A = `208/(x + 16)` hrs
iii. From the given information,
`216/x - 208/(x + 16) = 2`
`(216x + 3456 - 208x)/(x(x + 16)) = 2`
`(8x + 3456)/(x(x + 16)) = 2`
4x + 1728 = x2 + 16x
x2 + 12x – 1728 = 0
x2 + 48x – 36x – 1728 = 0
x(x + 48) – 36(x + 48) = 0
(x + 48)(x – 36) = 0
x = – 48, 36
But, speed cannot be negative.
So, x = 36.
iv. Speed of train = (36 + 16) km/hr = 52 km/hr.
APPEARS IN
RELATED QUESTIONS
The speed of an ordinary train is x km per hr and that of an express train is (x + 25) km per hr.
- Find the time taken by each train to cover 300 km.
- If the ordinary train takes 2 hrs more than the express train; calculate speed of the express train.
If the speed of a car is increased by 10 km per hr, it takes 18 minutes less to cover a distance of 36 km. Find the speed of the car.
If the speed of an aeroplane is reduced by 40 km/hr, it takes 20 minutes more to cover 1200 km. Find the speed of the aeroplane.
A girl goes to her friend’s house, which is at a distance of 12 km. She covers half of the distance at a speed of x km/hr and the remaining distance at a speed of (x + 2) km/hr. If she takes 2 hrs 30 minutes to cover the whole distance, find ‘x’.
A goods train leaves a station at 6 p.m., followed by an express train which leaved at 8 p.m. and travels 20 km/hour faster than the goods train. The express train arrives at a station, 1040 km away, 36 minutes before the goods train. Assuming that the speeds of both the train remain constant between the two stations; calculate their speeds.
A plane left 30 minutes later than the schedule time and in order to reach its destination 1500 km away in time, it has to increase its speed by 250 km/hr from its usual speed. Find its usual speed.
Some school children went on an excursion by a bus to a picnic spot at a distance of 300 km. While returning, it was raining and the bus had to reduce its speed by 5 km/hr and it took two hours longer for returning. Find the time taken to return.
The given table shows the distance covered and the time taken by a train moving at a uniform speed along a straight track:
| Distance (in m) | 60 | 90 | y |
| Time (in sec) | 2 | x | 5 |
The values of x and y are:
The speed of train A is x km/h and speed of train B is (x – 5) km/h. How much time will each train take to cover 400 km?
The speed of a boat in still water is 15 km/h and speed of stream is 5 km/h. The boat goes x km downstream and then returns back to the point of start is ______.
