Distance From House to Bus Station

Mr. Kasberg rides his bike at 6 mph to the bus station. He then rides the bus to work, averaging 30 mph. If he spends 20 minutes less time on the bus than on the bike, and the distance from his house to work is 26 miles, what is the distance from his house to the bus station?

This one is tricky.

Let me see.

House to bus station on bike:

rate = 6 mph

time = x

Bus station to work:

rate = 30 mph

time = x - (1/3)

Note: 20 minutes is 1/3 of an hour.

Distance from House to work is 26 miles.

Stuck here....

 

Convert 20 min to hrs: 20/60 = 1/3 hr

Let t = time on the bike

then

t-(1/3) = time on the bus

Write a dist equation

Dist = speed * time:

Bike dist + bus dist = 26 mi

6t + 30[t-(1/3)] = 26
6t + 30t - 10 = 26
36t = 26 + 10
36t = 36
t = 1 hr on the bike

6 mph for 1h = 6 mi from house to the bus station

Check solution by finding the distance
6(1) + 30(2/3) =
6 + 20 = 26 mi

 

Thank you. This problem is a bit wordy and thus tricky.

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