SOLUTION: A car travels at 40km/h or 60km/h to get from A to B, which is 30km away. The average speed for the entire journey is 45km'h. FInd the time and distance spent travelling at 40km/h

Question 1127167: A car travels at 40km/h or 60km/h to get from A to B, which is 30km away. The average speed for the entire journey is 45km'h. FInd the time and distance spent travelling at 40km/h
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x = the amount of time traveling at 40 kmph.
let y = the amount of time traveling at 60 kmph.

you are given that the total distance traveled is 30 km.

you are also given that the average speed for the entire journey is 45 kmph.

rate * time = distance.

your first equation is 40x + 60y = 30
your second equation is 45z = 30
your third equation is x + y = z

the first two equations conform to the general rule that rate * time = distance.

the third equation states that the amount of time traveling at 40 kmph plus the amount of time traveling at 60 kmph must be equal to the total time traveling at 45 kmph since the average overall speed is given as 45 kmph.

first solve for z in the third equation to get z = 30/45 = 2/3.

next replace z in the second equation with 2/3 to get x + y = 2/3.

next solve for x or y in the second equation.
i solved for y to get y = 2/3 - x

next replace y with 2/3 - x in the first equation to get 40x + 60 * (2/3 - x) = 30.

next solve for x in the first equation as follows:

start with 40x + 60 * (2/3 - x) = 30.
simplify to get 40x + 40 - 60x = 30.
combine like terms to get -20x + 40 = 30
add 20x to both sides of this equation and subtract 30 from both sides of this equation to get 40 - 30 = 20x
combine like terms to get 10 = 20x
divide both sides of this equation by 20 to get 1/2 = x.

next replace x with 1/2 in the third equation to get 1/2 + y = z
since z was already found to be equal to 2/3, this equation becomes 1/2 + y = 2/3
subtract 1/2 from both sides of this equation to get y = 2/3 - 1/2.
2/3 is equivalent to 4/6 and 1/2 is equivalent to 3/6, therefore y = 2/3 - 1/2 becomes y = 4/6 - 3/6 which results in y = 1/6.

you now have x = 1/2 and y = 1/6.

to confirm these values solve the problem, replace x and y in the first equation to get 40 * 1/2 + 60 * 1/6 = 30 which becomes 20 + 10 = 30 which becomes 30 = 30.

this confirms the solution is good.

you were asked to find the time and distance traveled at 40 kmph.

your solution is the the time traveled at 40 kmph is 1/2 hour and the distance traveled at 40 kmph is 20 kilometers.

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