A cyclist travels at a constant speed of 22.0 km/hr except for a 20 minute stop. The cyclist's average speed was 17.5 km/hr. How far did the cyclist travel?

Answer 1

Hi Ayush J.,

Lets write down what we know about the cyclist.

Constant speed, |v| = 22.0 km/hr.

Average speed, v_avg = 17.5 km/hr.

And a 20 minute stop, 20/60 hr or 1/3 hr.

We also know total distance is equal to constant speed times time , x = |v|*t or t = x/|v|.

Also the average speed is equal to the change in distance divided by the change in time v_avg = Δx/Δt or

Δt = Δx/v_avg.

In this problem the change in distance is equal to the total distance Δx = x, but total change in time is not equal to the time of constant speed Δt ≠ t, the total change in time is equal to the time at constant speed plus the stop, Δt = x\|v| + 1/3 hr. From this we can solve for x, the distance traveled.

Δt = x\|v| + 1/3 hr

x/v_avg = x/|v| + 1/3 hr

x/v_avg - x/|v| = 1/3 hr

x * (1/v_avg - 1/|v|) = 1/3 hr

x = 1/3 hr / (1/v_avg - 1/|v|)

Plug and chug:

x = 1/3 hr / ( 1/17.5 km/hr -1/22.0 km/hr)

x = 28.5 km

I hope this helps, Joe.