Daniel lives 27 miles from work. During the summer, he rides his bike at 8 mph to the metro station. He then takes the metro to work, which travels at 39 mph. If he spends 12 minutes less on the metro than on his bike, what is the distance from his house to the metro

The distance from his house to the metro is 3.27 miles

Explanation:

Daniel lives 27 miles from work.

Total distance traveled by Daniel = 27 miles

He rides his bike at 8 mph to the metro station

Let the distance to metro station be s miles and time taken be t hours.

We have

s = 8t

He then takes the metro to work, which travels at 39 mph. If he spends 12 minutes less on the metro than on his bike

Time taken = t + 12 minutes = (t + 0.2) hours

Remaining distance = 27 - s

27 - s = 39 ((t + 0.2)

27 - 8 t = 39t + 7.8

47t = 19.2

t = 0.409 hours

s = 8 x 0.409 = 3.27 miles

The distance from his house to the metro is 3.27 miles