Question 1
A train covered the first 5 km of its journey at a speed of 30 km/hr and the next 15 km at a speed of 45 km/hr. The average speed of the train was:
Explanation
Time for first leg = 530 = 16 hr
Time for second leg = 1545 = 13 hr
Total time = 16 + 13 = 12 hr. Total distance = 20 km
Average speed = 201/2 = 40 km/hr
Time for second leg = 1545 = 13 hr
Total time = 16 + 13 = 12 hr. Total distance = 20 km
Average speed = 201/2 = 40 km/hr
Question 2
A man travels from Delhi to Agra at an average speed of 30 km per hour and back at an average speed of 60 km per hour. What is the average speed for the whole journey?
Explanation
For an equal-distance two-leg journey, average speed = 2 × s1 × s2s1 + s2
= 2 × 30 × 6030 + 60 = 360090 = 40 km/hr
= 2 × 30 × 6030 + 60 = 360090 = 40 km/hr
Question 3
Aman walks a certain distance at a certain speed. If he walks 1/2 km an hour faster, he takes 1 hour less. But if he walks 1 km an hour slower, he takes 3 more hours. Find the distance covered by the man and his original rate of walking.
Explanation
Let original speed = s, time = t, distance = d = st.
(s + 0.5)(t - 1) = d ⇒ -s + 0.5t - 0.5 = 0 ⇒ t = 2s + 1
(s - 1)(t + 3) = d ⇒ 3s - t - 3 = 0 ⇒ t = 3s - 3
Equating: 2s + 1 = 3s - 3 ⇒ s = 4
t = 2(4) + 1 = 9
Distance = st = 4 × 9 = 36 km
(s + 0.5)(t - 1) = d ⇒ -s + 0.5t - 0.5 = 0 ⇒ t = 2s + 1
(s - 1)(t + 3) = d ⇒ 3s - t - 3 = 0 ⇒ t = 3s - 3
Equating: 2s + 1 = 3s - 3 ⇒ s = 4
t = 2(4) + 1 = 9
Distance = st = 4 × 9 = 36 km
Question 4
A lady travels at a speed of 20 km/h and returns at a quicker speed. If her average speed for the whole journey is 24 km/h, find the speed of the return journey (in km/h).
Explanation
For a round trip with speeds s1 and s2, average speed = 2 × s1 × s2s1 + s2
2 × 20 × s220 + s2 = 24
40s2 = 24(20 + s2)
40s2 = 480 + 24s2
16s2 = 480
s2 = 30
2 × 20 × s220 + s2 = 24
40s2 = 24(20 + s2)
40s2 = 480 + 24s2
16s2 = 480
s2 = 30
