#### PMTSTUMPED

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Thanks

- Thread starter PMTSTUMPED
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Thanks

Here's a back-door approach to this problem . . .

Adelle travels to Boston in 10 hours by bus. She returns in 20 hours by car.

If she went 10 mph faster by bus, how far did she travel to Boston?

The bus' speed is 10 mph more than the car's speed: .\(\displaystyle \text{bus} \:=\:\text{car} + 10\) .[1]

The bus drove the same distance in

The bus' speed must be

Substitute [2] into [1]: . \(\displaystyle 2\times\text{car} \:=\:\text{car} + 10 \quad\Rightarrow\quad \text{car} \:=\:10\)

The car drove for 20 hours at 10 mph.

The distance is: .\(\displaystyle 20 \times 10 \:=\:200\text{ miles.}\)

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Let v = speed of the carPMTSTUMPED said:

Thanks

and v + 10 = speed of the bus

20v = 10(v + 10)

20v = 10v + 100

10v = 100

v = 10

10v = 200

10(10 + 10) = 10(20) = 200

200 mi is the distance to Boston.