What are the average speeds each way for going 40 miles and 30 miles?

Question

You commute to work at a distance of 40 miles and return on the same route at the end of the day. Your average speed on the return trip is 30 miles per hour faster than your average speed on the morning’s outgoing trip. If the round trip takes 2 hours, what are your average speeds each way?

Answer 1

2 hours total for round trip

of total 40 miles

30 mph faster on return trip

what is average speed each way??

d =rt = distance = rate of speed times time

= 2r = 2 times average rate of speed = 40, miles

r = 20 mph

40/x + 40/(x+30) = 2

20/x + 20/(x+30 = 1

20x +600 +20x = x^2 +30x

x^2-10x -600=0

(x-30)(x+20) = 0

x = 30 mph

x+30 = 60 mph on return trip

40/60 = 2/3 hr on return trip

40/30 = 1 1/3 hr going, total 2 hours round trip

Answer 2

2 hours total for round trip

of 40 miles each way

30 mph faster on return trip

what is average speed each way??

d =rt = distance = rate of speed times time

t = d/r

40/x + 40/(x+30) = 2

20/x + 20/(x+30 = 1

20x +600 +20x = x^2 +30x

x^2-10x -600=0

(x-30)(x+20) = 0

x = 30 mph

x+30 = 60 mph on return trip

40/60 = 2/3 hr on return trip

40/30 = 1 1/3 hr going, total 2 hours round trip