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[Solved] Proportions

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A courier van delivers a package from office A to office B. If the van travels the 20 miles between the two offices at 50 miles per hour, how fast must the van travel on the return trip if the round- trip travel time is to be 40 minutes?
A) 55 mph
B) 60 mph
C) 65 mph
D) 70 mph
E) 75 mph

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Topic starter

Make a Rate Pie! Plug in 20 miles for distance on top, and 50 miles per hour for the rate. The time it takes is then  \small \frac{20}{50}=\frac{2}{5}   hour or   \small \frac{2}{5}(60)=24

minutes. The round-trip time needs to be 40 minutes, so the time we have left for the return trip is 40-24=16 minutes, which is \small \frac{16}{60}=\frac{4}{15}  hour.

So now we can make another Rate Pie, for the distance of 20 miles, and time of 4/15 hours, so the rate is    \small \frac{20}{\frac{4}{15}}=20*\frac{15}{4}=75    miles per hour.

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