Question

Sisters Joanne and Tracy specialize in two different triathlon events. Joanne finds that her average cycling speed is 14 mph faster than Tracy's average running speed. Joanne can cycle 60 miles in the same time that it takes Tracy to run 25 miles. If Tracy's running speed is n miles per hour, solve for n.

A) n = 10 mph
B) n = 12 mph
C) n = 15 mph
D) n = 18 mph

Answer 1

Tracy's running speed is determined by setting up an equation based on the given information about Joanne's cycling speed and the distances they travel. Solving the equation reveals that Tracy's running speed is 10 mph.

Step-by-step explanation:

To solve for Tracy's running speed, we can set up an equation based on the given information.

Let n be Tracy's running speed in miles per hour (mph). According to the problem, Joanne's cycling speed is 14 mph faster than Tracy's running speed, so Joanne's cycling speed is n + 14 mph.

We are given that Joanne can cycle 60 miles in the same time it takes Tracy to run 25 miles. Since speed is the ratio of the distance covered to the time taken, we can equate the time it takes for both sisters to travel these distances at their respective speeds:

1. Time = Distance / Speed
2. Joanne's time = 60 / (n + 14)
3. Tracy's time = 25 / n
4. 60 / (n + 14) = 25 / n

By cross multiplying, we get:

60n = 25(n + 14)

60n = 25n + 350

35n = 350

n = 350 / 35

n = 10 mph

Therefore, Tracy's running speed is 10 mph.