when driving to their family reunion, river's mom drove 10 miles at a rate of x mph and then 25 miles at a rate of x+10

Question

when driving to their family reunion, river's mom drove 10 miles at a rate of x mph and then 25 miles at a rate of x+10 mph. the total driving time was 45 minutes. what were the two driving speeds at which river's mom drove

Answer 1

35 miles in 45 minutes = 35 milers per 3/4 hour

35/3/4 = 35(4/3) = 140/3 = 46 2/3 mph average speed over the total distance

10 miles at x mph, 25 at 10 mph faster

d =rt, distance = rate of speed times time

35 = 10 +25 = xt + (x+10)(3/4 -t)= (41 2/3)(6/25) + (51 2/3)(3/4-7/31)

speed of 10 miles at 41 2/3 mph

speed for 25 miles at 51 2/3 mph

46 2/3 is average of x and x+10 = (2x+10)/2 = x +5

x = 41 2/3

x+10 = 51 2/3