Need help with applications of rational equations

Question

I need help with understanding how to answer this question.

 

The Iditarod trail sled dog race is an annual race that spans the Iditarod trail in Alaska. Teams of sled dogs race a distance of 1049 mi (miles)! The race record is a finishing time of 8 d, 19 h, 46 min, and 39 s. 

 

One particular leg of the race spans 200km. One team covered this span at a rate of 10 km/h faster on the way there than on the way back. If the total time for the trip was 9 h, what was the team's average speed on the way back? 

Answer 1

assume speed going up is (x + 10)

speed coming back is x

they covered the same distance up and back which is 200 km each leg

t1 (time going up) + t2 (time coming back) = 9 hours

 

find x?

 

time = distance / speed

t1 (200 km / x+10) + t2 (200 km / x) = 9

multiply both sides by x (x+10), then you get

200 x + 200 (x+10) - 9x (x+10) = 0

simplify

9x^2 - 310x - 2000 = 0

(9x + 50)(x - 40)=0

since speed cannot be negative, then there is one solution and that is x = 40 km/hr

 

check

 

t1 = 200 / (40 + 10) = 4 hours

t2 = 200 / 40 = 5 hours

t1 + t2 = 9 hours (this is right)

 

Let me know if you have questions. All the best