Question

Lisa can travel 228 miles in the same time that Kim travels 168 miles. If Lisa's speed is 15 mph faster than Kim's, find their rates.

Answer 1

• Lisa: 57 mph
• Kim: 42 mph

Explanation:

You want the speeds of Lisa and Kim if Lisa's speed is 15 mph faster than Kim's and they can travel 228 miles and 168 miles, respectively, in the same time.

Time

Let L represent Lisa's speed. Their travel time is the distance divided by the speed, so you have ...

228/L = 168/(L -15)

228(L -15) = 168L

60L = 228(15) . . . . . . . . add 228·15 -168L

L = 228(15/60) = 57

L -15 = 42

Lisa's speed is 57 miles per hour; Kim's is 42 mph.

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Additional comment

The distance traveled is proportional to speed when the travel time is constant. This means we can write the ratio of speeds as ...

228/168

We note that these differ by 60 "ratio units". The actual speeds differ by 15 mph, so each mile per hour is represented by (60/15) = 4 "ratio units". Dividing the ratio numbers by 4 gives the speed numbers:

228 : 168 = (228)(1/4) : (168)(1/4) = 57 : 42

The latter two numbers differ by 15, as do Lisa's and Kim's speeds.

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