A high-speed express train travels a distance of 180\text{ miles} in 1.5\text{ hours} at a… — ACT

A high-speed express train travels a distance of $180\text{ miles}$ in $1.5\text{ hours}$ at a constant speed. For an express schedule, its speed is increased by $20\%$ . At this new constant speed, how many miles will the train travel in $2.5\text{ hours}$ ?

A
$216\text{ miles}$
B
$300\text{ miles}$
$360\text{ miles}$ Answer
D
$375\text{ miles}$
E
$450\text{ miles}$

Answer

360\text{ miles}

The original speed is found by dividing

180\text{ miles}

1.5\text{ hours}

, which equals

120\text{ miles per hour}

. Increasing this speed by

20\%

yields

120 \times 1.20 = 144\text{ miles per hour}

. Multiplying the new speed of

144\text{ miles per hour}

2.5\text{ hours}

gives

360\text{ miles}

Step-by-Step Solution

Calculate the original speed of the train in miles per hour.

Original speed =

\frac{180\text{ miles}}{1.5\text{ hours}} = 120\text{ miles per hour}

Dividing total distance by total time gives the original unit rate.

Calculate the new speed after a

20\%

increase.

New speed =

120 \times (1 + 0.20) = 120 \times 1.20 = 144\text{ miles per hour}

Increasing a quantity by

20\%

is equivalent to multiplying it by

1.20

Calculate the distance traveled at the new speed in

2.5\text{ hours}

Distance =

144\text{ miles per hour} \times 2.5\text{ hours} = 360\text{ miles}

Multiplying the new rate by the new time yields the total distance.

Key Concept

Unit Rates and Proportional Scaling

Estimated Time:1m 15s

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