Question

a car goes uphill at the rate of 30 km an hour and downhill at the rate of 50km an hour .after 15hours it has covered 650km .how long does it go downhill and uphill respectively

Answer 1

The solution for this question is as follows:

The key point you have to note is that the distance covered  = speed x time taken

total time taken = 15 hours

Therefore if time taken going uphill is x hours , then time taken going downhill will be (15 - x)hours

distance = speed x time taken

Equation for distance going uphill:

 = time taken going uphill x speed for travelling uphill
 = x hours × 30km/hr
 = 30x km

Equation for distance going downhill:

= time taken going downhill × speed for downhill
= (15-x) 50km/hr
=(750-50x)km

the total distance = 650km

Therefore total distance uphill + distance downhill = 650km

750-50x + 30x = 650
750 - 20x = 650
20x =100
x= 5

Therefore time taken going uphill = 5 hours
and time take going down hill = 15hours - 5 hours = 10 hours.