Question

The average speed of one airplane is 200 mph faster than that of an automobile. If the automobile starts at 3 a.m. and the airplane starts from the same place at 11 a.m., they will have traveled the same number of miles by 1:00 p.m.

If r represents the rate of the automobile, how many miles does the plane travel?

200r
2(200 + r)
10r

Answer 1

lets make an equation for the car and the airplane.
distance = rate * time

Answer 2

Okay...

Answer 3

How?

Answer 4

How about this.
Let
d1 = distance car travels
r1 = rate of car,
t1 = number of hours the car travels.

d2 = distance plane travels
r2 = rate of plane
t2 = number of hours plane travels

Therefore we have car equation:
d1 = r1 * t1

plane equation
d2 = r2 * t2

Answer 5

d1 stands for a subscript
$$ d_1 $$

Answer 6

we are given two pieces of information,
r2 = r1 + 200
and that
d1 = d2 at 1 P.M.

Answer 7

At 1 PM the car has traveled 10 hours, since it started driving at 3 A.M.
At 1 PM the plane has traveled 2 hours, since it started flying at 11 AM.

Therefore we have :
d1 = r1 * t1
d2 = (200 + r1) * t2

and substituting time t1 = 10, and t2 = 2, d1 = d2
r1 * (10) = ( 200 + r1) * 2

Answer 8

So it's 2(200 + r) ..?

Answer 9

correct , since r1 is the same as r in the directions

Answer 10

but d1 = 10r , so it is also 10 r

Answer 11

Thanks so much for explaining it to me:)

Answer 12

also you can solve that equation for r , you might as well.

10 r = 2 ( 200 + r)
10r = 2*200 + 2r

8r = 400
r = 400 / 8 = 50 mph

so the plane went 250 mph , since it is 200 mph faster than the car rate r.

and you can see that 10 * 50 = 500 miles
2 ( 200 + 50) = 2 * 250 = 500 miles

so it works :)

Answer 13

Yes it sure does..! :) I appreciate all the help. I might need some more help in a little while. Would you mind assisting me again?

Answer 14

sure

Answer 15

Okie dokie! I'll let you know