Find their rates of travel

Steve travels 5 times as fast as Kevin. Traveling in opposite directions, they are 390 miles apart after 5 hours. Find their rates of travel.

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This is a distance, rate, time problem.

d = rt
distance = rate x time

Kevin
distance = d {unknown}
rate = r
time = 5 {they travel for 5 hours}
d = 5r {distance equals rate x time}

Steve
distance = d {unknown}
rate = 5r {Steve travels 5 times as fast as Kevin}
time = 5 {they travel for 5 hours}
d = 5r(5) {distance equals rate x time}
d = 25r {multiplied 5r by 5}

They are traveling in opposite directions. After 5 hours their distances add up to 390.
Add their distances together and set equal to 390.

5r + 25r = 390 {added distances and set equal to 390}
30r = 390 {combined like terms}
r = 13 {divided each side by 30}
5r = 65 {substituted 13, in for r, into 5r}

Kevin’s rate is 13 mph
Steve’s rate is 65 mph

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