A fast train takes 3 hours less than a slow train for a journey of 600 km. If…
2023
A fast train takes 3 hours less than a slow train for a journey of 600 km. If the speed of the slow train is 10 km/hr less than that of the fast train, then what are the respective speeds of the fast and slow trains?
Answer: A. 50 km/hr and 40 km/hr — CONCEPTFor a fixed distance, time equals distance divided by speed. When two objects cover the same distance, their time difference is the difference of these…
- A.
50 km/hr and 40 km/hr
- B.
30 km/hr and 20 km/hr
- C.
40 km/hr and 30 km/hr
- D.
More than one of the above
- E.
None of the above
Attempted by 6 students.
Show answer & explanation
Correct answer: A
CONCEPT
For a fixed distance, time equals distance divided by speed.
When two objects cover the same distance, their time difference is the difference of these quotients.
If their speeds differ by a known amount, express both speeds with one variable and solve the resulting equation.
APPLICATION
Let the speed of the fast train be x km/hr. Then the speed of the slow train is (x − 10) km/hr, where x > 10.
Their travel times for 600 km are 600/x hours and 600/(x − 10) hours respectively.
Since the slow train takes 3 hours more, 600/(x − 10) − 600/x = 3.
Combining the fractions gives 6000/[x(x − 10)] = 3, so x(x − 10) = 2000.
Therefore x2 − 10x − 2000 = 0, which factors as (x − 50)(x + 40) = 0.
A speed must be positive, so x = 50. Hence the speed of the slow train is 50 − 10 = 40 km/hr.
CROSS-CHECK
At 50 km/hr, 600 km takes 12 hours; at 40 km/hr, it takes 15 hours. The time gap is 3 hours and the speed gap is 10 km/hr, so both conditions hold.
RESULT
Therefore, the respective speeds of the fast and slow trains are 50 km/hr and 40 km/hr.