# word problem

#### PMTSTUMPED

##### New member
Adelle travels to Boston in 10 hours by bus. She turns in 20 hours by car. If she went 10 mph faster by bus, how far did she travel to Boston?
Thanks

#### soroban

##### Elite Member
Hello, PMTSTUMPED!

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 half the car's time.
The bus' speed must be twice the car's speed: .$$\displaystyle \text{bus} \:=\:2\times\text{car}$$ .[2]

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: .$$\displaystyle 20 \times 10 \:=\:200\text{ miles.}$$

#### fasteddie65

##### Full Member
PMTSTUMPED said:
Adelle travels to Boston in 10 hours by bus. She turns in 20 hours by car. If she went 10 mph faster by bus, how far did she travel to Boston?
Thanks
Let v = speed of the car
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.