A student walks at a speed of 5 km/hr from home and reaches his school at 7…
2017
A student walks at a speed of 5 km/hr from home and reaches his school at 7 a.m. When he walks at a speed of 6 km/hr, he reaches 15 minutes earlier. The distance between his home and his school is:
- A.
4.5 km
- B.
5.5 km
- C.
6.5 km
- D.
7.5 km
Attempted by 78 students.
Show answer & explanation
Correct answer: D
Solution:
Let the distance between home and school be d km.
Time taken at 5 km/h = d/5 hours.
Time taken at 6 km/h = d/6 hours.
The faster walk arrives 15 minutes = 0.25 hours earlier, so d/5 − d/6 = 0.25.
Compute the left side: d/5 − d/6 = d(1/5 − 1/6) = d/30. Therefore d/30 = 0.25.
Solve for d: d = 0.25 × 30 = 7.5 km.
Check: At 5 km/h time = 7.5/5 = 1.5 hours; at 6 km/h time = 7.5/6 = 1.25 hours. The difference is 0.25 hours = 15 minutes, so the result is correct.
Answer: 7.5 km.