Quadratic Speed Time Distance

Question

A car travels 20 kph faster than a truck. The car covers 350km in two hours less than time it takes truck to travel the same distance. what is the speed of the car? how about the truck?

Answer 1

Good morning,

 

r_c = rate that the car is traveling

 

r_t = rate that the truck is traveling

 

r_c -20 = r_t

 

set up an equation that compares the time traveled over the 350 km

 

distance/speed = time

 

350/(r_c)  + 2 = 350/r_t         this states the time for the car to go 350 km plus 2 equals the time for the truck

 

now substitute for r_t

 

350/r_c  + 2 = 350/(r_c -20)

 

the rest gets a bit tedious and there may be a faster way. Perhaps another tutor will add a quicker solution.

 

change the 2 to 2r_c/r_c so it can easily be added

 

350/r_c + 2r_c/r_c = 350/(r_c -20)

 

(350 + 2r_c) / r_c = 350/(r_c-20)

 

cross multiply

 

(350 + 2r_c)(r_c -20) = 350 r_c

 

350 r_c -7000 + 2r_c² -40r_c = 350r_c

 

2r_c² -40r_c -7000= 0

 

divide by 2

 

r_c² -20r_c -3500 = 0

 

factor 

 

(r_c -70)(r_c + 50) =0

 

r_c =70 and disregard the other answer because speed cannot be negative in this problem

 

the speed of the car is 70 and the speed of the truck is 50