SOLUTION: Two cars start from the same point, at 11:05 AM, traveling in opposite directions at 45 and 24 mph, respectively. At what time will they be 460 miles apart?

Question 1197566: Two cars start from the same point, at 11:05 AM, traveling in opposite directions at 45 and 24 mph, respectively. At what time will they be 460 miles apart?
Found 4 solutions by math_tutor2020, ewatrrr, MathTherapy, josgarithmetic:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Draw a number line. Point A is where both cars start.
Have point B to the left of A, and C to the right of A.
The cars will drive to B and C.
The goal is to have segment BC be 460 miles long.

Car #1 travels at 45 mph and goes from A to B
The distance from A to B is
distance = rate*time
distance = 45*t
where we don't know what the variable t is just yet

The distance from A to C is
distance = rate*time
distance = 24*t
which is what car #2 covers. We still don't know what t is, but it's the same t as before since we assume they started at the same time.

We have these segment lengths:
BA = 45t
AC = 24t

The two segment pieces must add to BC = 460, as this diagram shows

BA+AC = BC
45t+24t = 460
69t = 460
t = 460/69
t = 20/3 hours

At the time marker 20/3 hours, the two cars will be 460 miles apart.
Let's convert this to minutes only. Multiply by 60.
60*(20/3) = 400

20/3 hours = 400 minutes

Then let's convert to hours+minutes format
400 min = 360 min + 40 min
400 min = (360/60) hr + 40 min
400 min = 6 hr + 40 min

We'll add this duration onto the starting time 11:05 AM.

Add on 6 hours to go from 11:05 AM to 5:05 PM
Add on an additional 40 minutes to go from 5:05 PM to 5:45 PM

Answer: 5:45 PM

Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!

Hi D = rt (Total of their 'Distances = 460mi) Question States: 45t + 24t = 460 69t = 460 t = 6 2/3hr 2/3(60mim) = 40min At what time will they be 460 miles apart? 11:05AM + 6hr & 40min = 5:45pm Wish You the Best in your Studies.

Answer by MathTherapy(10556)   (Show Source): You can put this solution on YOUR website!

Two cars start from the same point, at 11:05 AM, traveling in opposite directions at 45 and 24 mph, respectively. At what time will they be 460 miles apart?

In this particular case, you can just DIVIDE the distance that they're eventually apart (460 miles), by the sum of the 2 speeds: () OR Let time it takes for both to be 460 miles apart be T Then when they're 460 miles apart, the faster and slower cars would've covered 45T and 24T miles, respectively We then get the following DISTANCE equation: 45T + 24T = 460 69T = 460 Time it takes the cars to be 460 miles apart, or 6 hours, 40 minutes, from 11:05 a.m. = 17:45, or 5:45 p.m. . It's TOTALLY SILLY and UNNECESSARY to convert to minutes and then back to hours and minutes, as the other person did! I hope you'll never do something like that!

Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!

RELATED QUESTIONS
Two cars start from the same point, at 9:45 am, traveling in opposite directions at 45... (answered by Alan3354)
Two cars, one traveling 12 mph faster-than the other, start at the same time from the... (answered by drj)
Two cars, one traveling 10 mph faster than the other, start at the same time from the... (answered by ewatrrr)
Two cars, one traveling 10 mph faster than the other car, start at the same time from the (answered by TimothyLamb,Danielshinmath)
Two cars leave from the same point, headed in opposite directions. Car A is traveling 50 (answered by jorel1380)
Two cars, one traveling 8 miles per hour faster than the other, start at the same time... (answered by JulietG)
plEase help! urgEnt! 1. Two cars start from the same point at the same time and travel (answered by Alan3354)
Two cars started from the same point and traveled for x hours in opposite directions at... (answered by Alan3354)
Two cars start from the same point and travel in opposite directions. One car is going... (answered by ewatrrr)