During a weekly training program, an athlete covers \frac{2}{5} of her total distance by c… — ACT

During a weekly training program, an athlete covers $\frac{2}{5}$ of her total distance by cycling and $35\%$ of her total distance by running. The remaining distance is completed by swimming. If she swims $15$ kilometers that week, what is her total training distance, in kilometers?

A
$20$
B
$37.5$
C
$45$
$60$ Answer
E
$75$

Answer

The athlete's total training distance for the week is 60 kilometers.

Converting

\frac{2}{5}

40\%

shows that cycling (

40\%

) and running (

35\%

) together account for

75\%

of the total training distance. Swimming accounts for the remaining

25\%

(

100\% - 75\%

). Since

25\%

of the total distance is

15

kilometers, dividing

15

0.25

yields the total distance of

60

kilometers.

Step-by-Step Solution

Convert the cycling fraction to a percentage.

\frac{2}{5} = 0.40 = 40\%

Converting all portions to percentages allows for easy summation and subtraction.

Calculate the total percentage covered by cycling and running combined.

40\% + 35\% = 75\%

Adding the cycling and running portions yields the covered percentage before swimming.

Find the percentage of the total distance that swimming represents.

100\% - 75\% = 25\%

The remaining portion of the whole (

100\%

) must equal the swimming percentage.

Set up an equation relating the swimming percentage to the actual distance and solve for total distance

T

0.25 \times T = 15 \implies T = \frac{15}{0.25} = 60

Dividing the part by its corresponding percentage rate gives the whole total distance.

Key Concept

Solving multi-step part-to-whole word problems by combining fractions and percentages.

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