Alejandro rode his bike to work at an average rate of 15 miles per hour. To go home, he put his bike on the front rack of the bus and took the bus home along the same route, traveling at an average rate of 22.5 miles per hour. If Alejandro’s bike ride to work took 45 minutes, how many hours did the bus ride home take?

0.25 hours
0.3 hours
0.5 hours
0.75 hours

3 answers

0.5 hours

Since his bike ride to work took 45 minutes (0.75 hours) at an average rate of 15 miles per hour, the distance he traveled is:
Distance = Rate x Time
Distance = 15 mph x 0.75 hours
Distance = 11.25 miles

To find how long the bus ride home took, we will use the distance he traveled and the average rate of 22.5 miles per hour:
Time = Distance / Rate
Time = 11.25 miles / 22.5 mph
Time = 0.5 hours

Therefore, the bus ride home took 0.5 hours.
Eitan is on a train heading west into the city while Dmitri is on a train on the adjacent track heading east, away from the city. They start 150 miles apart. Eitan’s train is traveling at an average speed of 65 miles per hour while the average speed of Dmitri's train is 55 miles per hour. How long will it take the two trains to reach each other? How far outside the city will they be?

The time when the two trains reach each other is
.

The trains are
away from the city when they reach each other.
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