SOLUTION: Car A starts in Sacramento at 11am. It travels along a 400 mile route to Los Angeles at 60 mph. Car B starts from Los Angeles at noon and travels to Sacramento along the same route

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Question 1209421: Car A starts in Sacramento at 11am. It travels along a 400 mile route to Los Angeles at 60 mph. Car B starts from Los Angeles at noon and travels to Sacramento along the same route at 75 mph. The route goes past Fresno which is 150 miles along the route from Los Angeles. How far from Fresno are the cars when they meet?
Found 3 solutions by ikleyn, mccravyedwin, greenestamps:
Answer by ikleyn(52800)   (Show Source):
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Car A starts in Sacramento at 11am. It travels along a 400 mile route to Los Angeles at 60 mph.
Car B starts from Los Angeles at noon and travels to Sacramento along the same route at 75 mph.
The route goes past Fresno which is 150 miles along the route from Los Angeles.
How far from Fresno are the cars when they meet?
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Let "t" be the time (in hours) for car A moving from S to LA to get the meeting moment. Then the time for car B moving from LA to S is (t-1) hours to get the meeting point (one hour less). The time equation for the meeting moment t is 60t + 75*(t-1) = 400 miles (the whole route length). Simplify and find t from this equation 60t + 75t - 75 = 400 60t + 75t = 400 + 75 135t = 475 t = 475/135 = 3.518519 hours. So, the time for the car B moving from LA to the meeting point is one hour less than that, i.e. 2.518519 hours. The distance from LA to the meeting point is 75*2.518519 = 188.888925 miles. It is 188.888925 -150 miles = 38.888925 miles from Fresno, between Fresno and Sacramento. ANSWER. The meeting point is 38.9 miles from Fresno, between Fresno and Sacramento.

Solved.

Answer by mccravyedwin(407)   (Show Source):
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Car A starts in Sacramento at 11am. It travels along a 400 mile route to Los Angeles at 60 mph. Car B starts from Los Angeles at noon... So Car A is already miles toward Los Angeles when car B starts. So at noon, when car B starts, they are miles apart. Car B starts from Los Angeles and travels to Sacramento along the same route at 75 mph. So their approach rate is mph, so their 340 miles of separation will shrink to 0, i.e., they will meet in hours after noon and when car B is miles from Los Angeles. The route goes past Fresno which is 150 miles along the route from Los Angeles. How far from Fresno are the cars when they meet? So they are 150 miles closer to Fresno than they are to Los Angeles by miles. So the answer is miles from Fresno. Edwin

Answer by greenestamps(13200)   (Show Source):
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Between 11am and noon, car A travels 60 miles (1 hour at 60mph). So at noon, when car B starts traveling, the two cars are 400-60 = 340 miles apart.

The ratio of the speeds of the two cars is 60:75 = 4:5, so when the cars meet car A has traveled 4/9 of the remaining 340 miles and car B has traveled 5/9 of that distance.

So the distance from Los Angeles that car B is when the cars meet is 5/9 of 340 miles.

(5/9)340 = 1700/9

Car B is 1700/9 miles from Los Angeles when the cars meet, and Fresno is 150 miles from Los Angeles. The distance from Fresno when the cars meet is then

1700/9 - 150 = 1700/9 - 1350/9 = 350/9 = 38 8/9 miles or about 38.9 miles.

ANSWER: The two cars are (about) 38.9 miles north of Fresno when the cars meet.