Question 553716: hi i need help in solvinf this worded question which has confused me in what i should do. I need help on the following question:
a car travels x km at 50 km/h and y km at 60 km/h. The total time taken is 5 hours. if the average speed for the journey is 56km/h, what are x and y?
i have already found the total distance of the journey which is 280km. how do i find x and y. thanks
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! rate * time = distance
for the total distance we get 56*5 = d which becomes 280 = d
total distance = 280 km.
you got that part right.
x equals the distance traveled at 50 kmph and y equals the distance traveled at 60 kmph.
we get:
x + y = 280
we also know from the formula of rate * time = distance that:
50T1 = x
60T2 = y
where T1 and T2 are the times to go distance x and distance y.
we know tht T1+ T2 = 5 hours.
this means that:
T1 + T2 = 5 hours
from the equation of 50T1 = x, we solve for T1 to get T1 = x/50
from the equation of 60T2 = y, we solve for T2 to get T2 = y/60
we substitute for T1 and T2 in the equaqtion of T1 + T2 = 5 hours to get:
x/50 + y/60 = 5
we have 2 equations that we need to solve simultaneously.
they are:
x + y = 280
x/50 + y/60 = 5
multiply both sides of the second equation by 60 to get:
60x/50 + 60y/60 = 5*60
this simplifies to:
(6/5)x + y = 300
our 2 equations are now:
x + y = 280
(6/5)x + y = 300
multiply the first equation by -1 and then add the 2 equations together to get:
(1/5)x = 20
divide both sides of this equation by (1/5) to get:
x = 100
if x = 100, and x + y = 280, then y = 180
we have:
x = 100
y = 180
the car travels for 100 miles at 50 miles per hours and 180 miles at 60 miles per hour to gain a total distance of 280 miles.
x + y becomes 100 + 180 which equals 280.
the car travels 100 miles at 50 miles per hour for 2 hours.
the car travels 180 miles at 60 miles per hour for 3 hours.
total time is 5 hours.
x/50 + y/60 = 5
100/50 + 180/60 = 5
figures check out so the answer is good.
x = 100
y = 180
time to travel 100 miles at 50 miles per hour is 2 hours.
time to travel 180 miles at 60 miles per hour is 3 hours.
total distance is 280
total time is 5 hours
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