If your friend leaves your house at a speed of 8mph and two hours later you follow in your car at 40mph, how long will It be before you catch up to your friend? How far did you both travel?

1/2 hour 20 miles

Step-by-step explanation:

Your friend has a head start of (2 h) * (8 mi/h) = 16 mi.

When you leave, you gain on your friend at the rate of 40 mph - 8 mph = 32 mph. So, it will take ...

(16 mi) / (32 mi/h) = 1/2 h

for you to reduce the distance between you to zero.

In that 1/2 hour, you have traveled ...

(1/2 h) * (40 mi/h) = 20 mi

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This is the same distance your friend has traveled in 2.5 hours at 8 mi/h.