Question

On Saturday morning, Ahmed decided to take a bike ride from one end of the 15-mile bike trail to the other end of the bike trail and back. His average speed the first half of the ride was 2 mph faster than his speed on the second half. Find an expression for Ahmed's total travel time. If his average speed for the first half of the ride was 12 mph, how long was Ahmed's bike ride? ​

Answer 1

The expression which relates the total time taken and the time taken for the trip is [15s + 15(s+2)] / s² + 2s and 2.32 hours respectively.

Travel time = distance ÷ speed

Second half of the trip :

• Speed = s mph

• Distance covered = 15 miles

Time taken for second half of trip :

Time taken = 15 / s

First half of the trip :

• Speed = s + 2 mph

Time taken for first half of trip :

Time taken = 15 / (s+2)

Total time taken :

First half + second half

15/(s+2) + 15/s = [15s + 15(s+2)] / s² + 2s

B)

If s = 12

Substitute s = 12 into the expression :

[15(12) + 15(12+2)] / 12² + 2(12)

[180 + 210] / 144 + 24

390 / 168

= 2.32 hours

Therefore, the total time taken is 2.32 hours.

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