Question

A bicyclist rides his bike each day on a trail not far from his house. During the first part of the ride he is pedaling mostly uphill and his average speed is 6 miles an hour. After a certain point, he is traveling mostly downhill and averages 15 miles per hour. If the total distance he travels is 30 miles and the total time he rides is 4 hours, how long did he ride at each speed?

Answer 1

total time, t = 4hours

1st speed, a = 6 mph

2nd speed, b = 15mph

total distance covered, d = 30miles

time spent at 6mph, x

time at 15mph, y

total time, t = x + y

=》4 = x +y...eqn 1

total dist, d = ax + by

=》30 = 6x + 15y...eqn 2

subst for y (= 4 -x) in eqn 2

30 = 6x + 15(4-x)

= 》 9x = 30

x = 3 1/3 = 3 hrs 20mins

y = 4 - 3 1/3 = 2/3 = 40mins