SOLUTION: The difference in the average speeds of two train is 25km/h, the faster train takes 2 hours less to travel 150km than the slower train takes to travel 125km. Find the speeds of the

Question 1118151: The difference in the average speeds of two train is 25km/h, the faster train takes 2 hours less to travel 150km than the slower train takes to travel 125km. Find the speeds of the two trains
Found 3 solutions by josgarithmetic, greenestamps, ikleyn:
Answer by josgarithmetic(39621)   (Show Source): You can put this solution on YOUR website!

SPEED TIME DISTANCE FASTER r+25 150/(r+25) 150 SLOWER r 125/r 125 DIFFERENCE 2

Equation to solve for the slower train speed

Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

Let the speed of the slower train be x; then the speed of the faster train is x+25.

The wording of the problem as given:
"the faster train takes 2 hours less to travel 150km than the slower train takes to travel 125km"

Translation into a mathematical sentence that can be turned directly into an equation:
"the time it takes slower train to go 125 km is 2 hours more than the time it takes the the faster train to go 150 km"

Translation (since time equals distance divided by rate):

If an algebraic solution is not required, I would definitely use logical trial and error to solve the problem. Since the difference in times is exactly 2 hours, the numbers in the problem have to be "nice" numbers. Looking at the equation, my first guess (because of the "125/x") would be x = 25 -- and it works:

125/25 = 5; 150/50 = 3; 5-3 = 2

If an algebraic solution is required, then I would multiply the whole equation by the least common denominator of all the fractions:

Factoring that quadratic equation would have been very time-consuming if I hadn't already known the answer....
Answer by ikleyn(52817)   (Show Source): You can put this solution on YOUR website!
.

Let x be the average speed of the slower train, in kilometers per hour. Then the speed of the faster train is (x+25) km/h. The slower train takes hours to travel 125 kilometers. The faster train takes hours to travel 150 kilometers. The condition says that the faster train takes 2 hours less: - = 2 hours. It is yours "time" equation. // As soon as I got this equation, I just know the answer: x = 25. (I solved the equation in my head) // But I will pretend that I don't know the solution, and will solve it formally (i.e. "honestly") To solve it, multiply both sides by x*(x+25). You will get 125*(x+25) - 150*x = 2x*(x+25), 125x + 125*25 - 150x = 2x^2 + 50x, 2x^2 + 75x - 125*25 = 0, 2x^2 - 50x + 125x - 125*25 = 0, <<<---=== starting from this line, I work to factor left side 2x*(x-25) + 125(x-25) = 0, (2x+125)*(x-25) = 0. The only positive root is x= 25, and it is the only solution to the problem. Answer. The slower train average speed is 25 km/h. The faster train 25+25 = 50 km/h. Check. - = 5 - 3 = 2. ! The time equation is satisfied !

Solved and checked.

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