SOLUTION: Ching leaves San Francisco and travels toward Los Angeles at 50 mi/h. An hour later, Phil leaves Los Angeles and travels toward San Francisco at 60 mi/h. If the two cities are 38

Question 55158: Ching leaves San Francisco and travels toward Los Angeles at 50 mi/h. An hour later, Phil leaves Los Angeles and travels toward San Francisco at 60 mi/h. If the two cities are 380 miles apart, how many hours will it take for Ching to meet Phil?
Found 3 solutions by checkley71, Hook, funmath:
Answer by checkley71(8403)   (Show Source): You can put this solution on YOUR website!
DISTANCE=RATE TIMES TIME
380=50T+60T
380=110T
T=380/110
T=3 5/11 HOURS LATER THEY MEET
PROOF
380=50(3 5/11)+60(3 5/11)
380=50*38/11+60*38/11
380=1900/11+2280/11
380=4180/11
380=380
Answer by Hook(36)   (Show Source): You can put this solution on YOUR website!
A couple questions to start? Why are Ching and Phil meeting in the Central Valley? There's nothing there? Why don't they agree to just have one person come to LA or SF. And 50 and 60 mph? You have got to be kidding me. Anything less than 75 on the I-5 is right out. Never mind that...on to the math.
Let's call t the number of hours since Ching smashes his foot on the gas.
We know that or just
How far does Ching go? That's easy:

What about Phil? We have to account for him leaving an hour later, so we put in place of .

Combined, the two have to equal 380 miles. We get this:

Distribute the 60

Combine like terms

Move the 60 to the right side

Divide by 110

It will take Ching 4 hours to meet Phil.
Four hours! That's insane. To get to the middle of nothing. If you press it from SF, you can get to the grapevine in 5 hours!
Answer by funmath(2933)   (Show Source): You can put this solution on YOUR website!
Ching leaves San Francisco and travels toward Los Angeles at 50 mi/h. An hour later, Phil leaves Los Angeles and travels toward San Francisco at 60 mi/h. If the two cities are 380 miles apart, how many hours will it take for Ching to meet Phil?
The formula for distance is , where d=distance, r=rate (or speed) and t=time
Ching's rate=50 mi/h
Ching's time=t
Ching's distance=50t
Phil's rate=60 mi/h
Phil's time=t-1 (Because he left an hour later, he drove an hour less.)
Phil's distance=60(t-1)
The total distance traveled=380 mi
Problem to solve for t:
50t+60(t-1)=380
50t+60t-60=380
(50+60)t-60=380
110t-60=380
110t-60+60=380+60
110t=440
110t/110=440/110
t=4
Ching will have to travel t=4 hrs.
(they didn't ask, but Phil would travelt-1=4-1=3hrs.)
Happy Calculating!!!
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