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Jack's father drives to work in 30 minutes when driving at his usual speed. When traffic is bad, he drives 30 miles per hour slower and the trip takes one hour longer. How far is Jack's fathers work from home.

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Answer:

22.5 miles

Step-by-step explanation:

No traffic :

Let speed = x

Time taken = 30 = 30/60 = 0.5 hour

Speed = distance / time

Distance = d

x = d / 0.5 - - - (1)

With traffic :

Speed = x - 30

Time taken = 1 hour 30 minutes = 1.5 hour

x - 30 = d / 1.5

x = d/1.5 + 30 - - - - (2)

Equating (1) and (2)

d / 0.5 = d/1.5 + 30

d /0.5 - d /1.5 = 30

(1.5d - 0.5d) / 0.75 = 30

1.5d - 0.5d = 22.5

1d = 22.5

Hence,

d = 22.5 miles

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