one day , hari walked along a circular track for 3 hours . he then cycled along the track for the time he would take to walk one round the track and thereby covered a total of 9 rounds . Another day, he walked along the track for 4 hours and then drove his motorcycle along the track for the time he would walk one round around the track and thereby covered a total of 14 rounds . if the speed of his cycling and motorcycle were 5km/hr and 10km/hr respectively,then find his walking speed.
A. 5km/hr
B. 6km/hr
C. 8k/hr
D . 2km/hr
Answers
Q. One day, Hari walked along a circular track for 3 hours. He then cycled along the track for the time he would take to walk one round the track and thereby covered a total of 9 rounds. Another day, he walked along the track for 4 hours and then drove his motorcycle along the track for the time he would walk one round around the track and thereby covered a total of 14 rounds. If the speed of his cycling and motorcycle were 5km/hr and 10km/hr respectively, then find his walking speed.
A. 5km/hr
B. 6km/hr
C. 8k/hr
D. 2km/hr
Solution :-
Let us assume that, Length of circular track is L km and walking speed is x km/h.
Day 1) :-
→ In 3 hours he travel distance by walking = 3x km .
now,
→ Time taken to complete one round = D/S = (L/x) hours.
given that,
→ Speed on cycle = 5km/h .
then,
→ Distance covered in time to complete one round in walking = S * T = 5 * (L/x) = (5L/x) km .
A/q,
→ Total distance = 9 rounds
→ 3x + (5L/x) = 9L
→ 3x² + 5L = 9xL --------- Eqn.(1)
Day 2) :-
→ In 4 hours he travel distance by walking = 4x km .
now,
→ Distance covered in time to complete one round in walking by motorcycle = S * T = 10 * (L/x) = (10L/x) km .
A/q,
→ Total distance = 14 rounds
→ 4x + (10L/x) = 14L
→ 4x² + 10L = 14xL --------- Eqn.(2)
Multiply Eqn.(1) by 4 and Eqn.(2) by 3 and subtracting the results from Eqn.(2) result ,
→ 3(4x² + 10L) - 4(3x² + 5L) = 3*14xL - 4*9xL
→ 12x² - 12x² + 30L - 20L = 42xL - 36xL
→ 10L = 6xL
→ 10 = 6x
→ x = (10/6)
→ x = (5/3) km/h (Ans.)
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