Question

Francesca plans to compete in a biathlon that involves running and cycling. During one training​ session, she covered a total distance of 46 miles in four hours. If she ran at a rate of 5 mph and cycled at a rate of 15 ​mph, how long did she spend​ cycling?

Answer 1

.

Explanation:

Use the distance formula

d = vt

where:

d = distance (miles)

v = speed (mph)

t = time (hours)

Let x = run time

Let y = bike time

Total time: x + y = 4

Using these variables we can write an equation representing the formula.

dTotal = drun + dbike

49 = 9x + 22y

Next, we get the equation in terms of only x or y. We'll get it in terms of x.

49 = 9x +22(4 - x)

49 = 9x + 88 - 22x

-39 = -13x

3 = x

Plug in this value of x into the variables to find the distance for each part.

run distance = 9x

bike distance = 22(4 - x)