Bill runs for 30 minutes at 8 mph and then runs for 15 minutes at 13mph. What was his average speed during his entire run?

Question

Bill runs for 30 minutes at 8 mph and then runs

for 15 minutes at 13mph. What was his average

speed during his entire run?

Answer 1

HI Khushi,

Thanks for your question!

Bill's average speed is the total distance he ran divided by the total time he spent running. The total time is easy to compute: it's the sum of the time spent running at 8 mph and the time spent running 13 mph, so we have

Toral Time = 30 min + 15 min = 45 min,

or 3/4 hr (if you convert to hours).

The total distance can be computed by computing the distance traveled when Bill was running at 8 mph, computing the distance traveled when Bill was running at 13 mph, and then adding these distances together. Using the distance = rate * time formula, we find

Toral Distance = (8 mph)*(1/2 hr) + (13 mph)*(1/4 hr) = 29/4 miles.

Note you have to convert minutes to hours because his speed is recorded in miles per hour (not miles per minute).

Finally, to compute Bill's average speed, we compute

Averge Speed = (Total Distance)/(Total Time) = (29/4 miles)/(3/4 hr) = 29/3 mph,

or approximately 9.67 mph. This makes intuitive sense, as we would expect Bill's average speed to be between 8 mph and 13 mph and closer to 8 mph (since he ran at that speed longer).