rate word problem

[wrightka]

Two towns are 420 miles apart. A car leaves the first town traveling towards the second town at 55mph. At the same time, a second car leaves the other towand heads toward the first town at 65mph. How long will it take for the two cars to meet?
rate of first car= 55mph
rate of second car= 65mph
total miles apart = 420miles
x= time for cars to meet
rate x time =distance
first car= 420m/55mph= 7.6 h
second car= 420/65= 6.5 h

answer is supposed to be 3.5 hours.

 

[Denis]

Keep it simple: 420 / (55 + 65) = 420 / 120 = 3.5 ; kapish?

 

[soroban]

Hello, wrightka!

Your set-up and reasoning are incorrect . . .

Two towns are 420 miles apart.
Car A leaves the town X traveling towards town Y at 55 mph.
At the same time, car B leaves town Y and heads toward town X at 65 mph.
How long will it take for the two cars to meet?

rate of first car = 55 mph
rate of second car = 65mph
total miles apart = 420 miles
x = time for cars to meet
rate x time = distance

Car A: (420 miles)/(55 mph) = 7.6 hours
Yes, If car A drove the entire 420 miles, it would take 7.6 hours.

Car B: (420 miles)/(65 mph) = 6.5 hours
And if car B drove the entire 420 miles, it would take 6.5 hours.

But is that what happened?

Each car drove part of the distance ... and together, they covered 420 miles.


Here's the reasoning . . .

Let \(\displaystyle x\) = number of hours for the cars to meet.

Car A drove \(\displaystyle x\) hours at 55 mph.
. . It drove: .\(\displaystyle 55x\) miles.

Car B drove for \(\displaystyle x\) hours at 65 mph.
. . It drove: .\(\displaystyle 65x\) miles.

Together, they covered 420 miles: .\(\displaystyle 55x + 65x \:=\:420\)

. . There is your equation !

 

[wrightka]

Oh, Wow! That helped a lot!!