Distance, rate, and time of two cyclists

Two cyclists, 90 km apart, start riding toward each other at the same time. One cycles twice as fast as the other. If they meet 2 hours later, at what average speed is each cyclist traveling?

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distance = rate x time
d = rt

one cyclist
rate = r
time = 2 {they meet in 2 hours}
d = 2r {distance = rate x time}

other cyclist
rate = 2r {cycles twice as fast as first}
time = 2 {they meet in 2 hours}
d = 4r {distance = rate x time}

When they meet, their combined distance is 90 km.
2r + 4r = 90 {added distances together and set equal to 90}
6r = 90 {combined like terms}
​r = 15 {divided each side by 6}

2r = 30 {substituted 15, in for r, into 2r}

one cyclist is traveling 15 km per hour
the other cyclist is traveling 30 km per hour

Ask the House
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