Solve the following word problem by calculating the missing value.

Answer:An engineering battalion can lay

40

feet of runway matting in

15

minutes. Operating at this constant rate, the battalion will lay 【240】 feet of matting in

1.5

hours.

240

Because

1.5

hours is equivalent to

90

minutes, the time period is exactly

6

times longer than the original

15

-minute period (

90 \div 15 = 6

). In a direct proportion, the amount of matting laid increases by the same factor, so

40 \text{ feet} \times 6 = 240 \text{ feet}

Convert the target time frame into the same units used for the known rate.

1.5 \text{ hours} = 1.5 \times 60 \text{ minutes} = 90 \text{ minutes}

Units of time must match to set up a valid direct proportion.

Set up a proportion relating feet of matting to minutes.

\frac{40 \text{ feet}}{15 \text{ minutes}} = \frac{x \text{ feet}}{90 \text{ minutes}}

Because the rate is constant, the ratio of distance to time remains the same.

Solve for the unknown value

x

x = \frac{40 \times 90}{15} = 40 \times 6 = 240

Isolating

x

provides the total feet of matting laid in

90

minutes.

Direct proportions with unit conversion

Question