Angela made the trip by bus in 16 hours and the return trip by car in 20 hours. A bus traveled 10 miles per hour faster than the car. How far was the trip? (Use the formula D=rt [Distance = rate x time])

Question

anonymous · Answer

Do you have any idea what to do?

anonymous · Answer

No I don't lol

anonymous · Answer

That's ok! :)

We have to set two equations: one for the car and one for the bus.

anonymous · Answer

FOR THE CAR:

time: 20 hours
rate: x


FOR THE BUS:

time: 16 hours
rate: 10+x $\text{(since it is 10 mph faster than the car)}$

anonymous · Answer

we know that d=rt
and e have to find the distance.

anonymous · Answer

EQUATION FOR THE CAR:
d=20x

EQUATION FOR THE BUS:
d=16 (10+x)

anonymous · Answer

Are you getting it?

anonymous · Answer

So far yes

anonymous · Answer

Okay cool! So now, equate the two equation since both of them have d=???

So...

$\huge 16(10 + x)=20x$

Now solve for x.

anonymous · Answer

Is it x = 8?

anonymous · Answer

$\huge 160+16x=20x$

anonymous · Answer

$\huge 160=4x$

What is $160 \div 4$?

anonymous · Answer

40

anonymous · Answer

Good! So we now know that x=40. Now, substitute it to either of the two equations:

EQUATION FOR THE CAR:
d=20x

EQUATION FOR THE BUS:
d=16 (10+x)

anonymous · Answer

800

anonymous · Answer

So the distance is 800. :)

anonymous · Answer

Thank you! Can you help me with another problem lol

anonymous · Answer

I can try lol

anonymous · Answer

It's not a distance problem, it's a percent problem

anonymous · Answer

Forty percent of the signs are circular. If 3600 signs are noncircular, how many signs are there in all?