SOLUTION: Car and a Truck leave point A. The car leaves point A at 9am.The truck leaves 45 mintues earlier.Car's speed 120km/h and the truck's speed is 90km/h.How far away will they meet?...

Question 1137133: Car and a Truck leave point A. The car leaves point A at 9am.The truck leaves 45 mintues earlier.Car's speed 120km/h and the truck's speed is 90km/h.How far away will they meet?...This is what i did.truck has a 67.5km head start.speed difference is 30km/h...far as i got ...can i have a step by step how to achieve this answer....Thanks tutors for all your wonderful help.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i think you were on the right track.

following your logic, i get the difference in speed is 30 kilometers per hour.

the truck is 67.5 kilometers ahead.

rate * time = distance.

rate is 30 and distance is 67.5.

solve for time to get time = distance / rate = 67.5 / 30 = 2.25 hours.

the car will catch up to the truck in 2.25 hours.

traveling at 120 kilometers per hour, the car will catch up to the truck when they have both traveled 120 * 2.25 = 270 kilometers.

the truck has traveled 45 minutes longer, which is 3/4 of an hour longer, so the truck has traveled for 3 hours at 90 kilometers per hour for a distance of 270 kilometers.

the solution checks out.

the solution is that the car will catch up to the truck in 270 kilometers.

i would have solved it a little differently but the answer should be the same.

i would have solved as follows.

rate * time = distance.

for the truck, rate * time = distance becomes 90 * T = D

for the car, rate * time = distance becomes 120 * (T - 3/4) = D

when the car catches up to the truck, they will have both traveled the same distance.

the truck is traveling 3/4 of an hour less time than the car.

these are two equations that need to be solved simultaneously.

they are:

90 * T = D
120 * (T - 3/4) = D

since they are both equal to D, then 90 * T must be equal to 120 * (T - 3/4), so you get:

90 * T = 120 * (T - 3/4).

simplify to get 90 * T = 120 * T - 90.

subtract 90 * T from both sides of he equation and add 90 to both sides of the equation to get 90 = 30 * T.

solve for T to get T = 90 / 30 = 3.

go back to the original equations and replace T with 3 to get:

90 * T = D becomes 90 * 3 = D which becomes 270 = D.

120 * (T - 3/4) = D becomes 120 * (3 - 3/4) = D which becomes 120 * 2.25 = D which becomes 270 = D.

two different methods which both tell you that the distance is 270 kilometers.

you can take your pick which one you prefer.

the key is that the basic equation involved is rate * time = distance.

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