Question 1199945: Hi
Towns c and d are 220km apart. A truck driver and a taxi driver start off at the same time c to d . The taxi driver reached d 5/3 hours ahead of the truck driver who still had 100km to go.
What was the speed of the truck driver.
Thank you
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52878)   (Show Source):
You can put this solution on YOUR website! .
Towns C and D are 220 km apart. A truck driver and a taxi driver start off at the same time C to D.
The taxi driver reached D 5/3 hours ahead of the truck driver
who still had 100 km to go. What was the speed of the truck driver.
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This problem seems to be complicated, but in reality it is extremely simple.
To find the solution, you simply should read the problem attentively
and understand what the problem really says.
It says that the truck covers the remaining 100 km in  hours.
Hence, the speed of the truck is  =  = 20*3 = 60 km/h. ANSWER
As always, to find the speed, we divide the traveled distance by the travel time.
Solved.
-----------------
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started at the same time etc.) is EXCESSIVE and UNNECESSARY
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Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! towns C and D are 220 km apart.
rate * time = distance.
taxi drives at a rate of B kph.
truck drives at a rate of A kph.
the time it takes the truck to make the distance between C and D = T.
the time it takes the taxi to make the distance between C and D = T - 5/3.
you are also given that the truck had 100 kilometers to go when the taxi arrived at the destination.
the equation for the taxi is B * (T - 5/3) = 220
thre eqution for the truck is A * T = 220
since the truck still had 100 km to go when the taxi arrive at the destination, you are also given the equation:
A * (T - 5/3) = 220 - 100 which becomes:
A * (T - 5/3) = 120
the two equationt so solve simultaneously are:
AT = 220
A * (T - 5/3) = 120
simplify to get:
AT = 220
AT - 5/3A = 120
replace AT in the second equatin with 220 to get:
220 - 5/3A = 120
subtract 120 from both sides of the equation and add 5/3A to both sides of the equation to get:
220 - 120 = 5/3A
simplify to get 100 = 5/3A
solve for A to get:
A = 100 * 3.5 = 60.
this tells you that the rate of the truck is 60 kilometers per hour.
from that you can solve for time to get:
60 * T = 220
T = 220 / 60 = 22/6
from B * (T - 5/3) = 220, replace T with that to get:
B * (22/6 - 5/3) = 220
solve for B to get:
B = 220 / (22/6 - 5/3) = 110 kph.
that's the speed of the taxi.
you get:
speed of the truck is 60 kph.
speed of the taxi is 110 kph.
confirm as shown below.
the taxi travels at 110 kph for (T - 5/3) hours.
since T = 22/6, you get:
the taxi travels at 110 kph for (22/6 - 5/3) hours = 110 * (22/6 - 5/3) = 220 kilometers.
the truck travels at 60 kph 22/6 hours = 60 * 22/6 = 220 kilometers.
in the same number of hour that the taxi travels 220 kilometers, the truck travels 60 * (22/6 - 5/3) = 120 kilometers.
the truck still have 100 kilometers to go when the taxi has finished the journey.
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