Question

Elvira and Aletheia live 3.1 miles apart on the same street. They are in a study group that meets at a coffee shop between their houses. It took Elvira 12 hour and Aletheia 23 hour to walk to the coffee shop. Aletheia's speed is 0.6 miles per hour slower than Elvira's speed. Find both women's walking speeds.

Answer 1

• Elvira's speed: 3.0 mph
• Aletheia's speed: 2.4 mph

Explanation:

Let "e" and "a" represent the speeds of Elvira and Aletheia, respectively. Then the total distance they cover is ...

distance = speed × time

(1/2)e + (2/3)a = 3.1

And the relationship between their speeds is ...

e - a = 0.6

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To solve this system, we can double the first equation and subtract the second to get ...

2(1/2e +2/3a) -(e -a) = 2(3.1) -(0.6)

7/3a = 5.6 . . . . . . . . . . simplify

a = (3/7)(5.6) = 2.4 . . . multiply by 3/7

e = a +0.6 = 3.0 . . . . . Elvira's speed is 0.6 mph more than Aletheia's

Elvira's walking speed is 3.0 miles per hour; Aletheia's is 2.4 miles per hour.