A long-distance runner is training for an upcoming race. On Monday, she completed \frac{2}… — ACT

A long-distance runner is training for an upcoming race. On Monday, she completed $\frac{2}{5}$ of her total weekly distance goal. On Tuesday, she completed $0.35$ of her total weekly distance goal. If she has $12$ miles left to complete her weekly goal, what is her total weekly goal distance, in miles?

A
16
B
21
C
30
48Answer
E
60

Answer

48 miles

Converting

\frac{2}{5}

0.40

gives a total completed portion of

0.40 + 0.35 = 0.75

of the goal. The remaining portion is

1 - 0.75 = 0.25

of the total goal. Setting

0.25 \times \text{total goal} = 12

miles gives a total weekly goal of

\frac{12}{0.25} = 48

miles.

Step-by-Step Solution

Convert the fraction completed on Monday to a decimal

\frac{2}{5} = 0.40

Converting all completed portions to decimals allows for direct addition.

Calculate the total portion of the weekly goal completed on Monday and Tuesday

0.40 + 0.35 = 0.75

Summing Monday's and Tuesday's completed portions gives the total completed fraction of the goal.

Determine the remaining fraction of the weekly goal

1 - 0.75 = 0.25

Subtracting the completed portion from the total whole (1.00) yields the fraction remaining.

Set up an equation relating the remaining fraction to the remaining miles to find the total goal distance

x

0.25x = 12 \implies x = \frac{12}{0.25} = 48

Dividing the remaining distance by the remaining fraction yields the total weekly goal distance.

Key Concept

Combining fractions and decimals to determine a total quantity from a remaining part

Estimated Time:1m 15s

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