find the two rates.

Question

Gemma recently rode her bicycle to visit her friend who lives 1212 miles away. On her way there, her average speed was 77 miles per hour faster than on her way home. If Gemma spent a total of 11 hour bicycling, find the two rates.

Answer 1

Distance = Rate*time.... d = rt

 

1212 = rt

1212 = (r-77)(11-t)

 

From 1st equation, t = 1212/r

 

1212 = (r-77)(11-1212/r)

1212 = 11r - 1212 - 11(77) + 77(1212)/r

1212 + 1212 + 11(77) = 11r + 77(1212/r)

3271 = 11r + 93324/r

3271r = 11r² + 93324

 

11r² - 3271r + 93324 = 0

 

r = [3271 ±√((-3271)²-4(11)(93324))]/2(11)

 

r = (3271 ±√(6593185))/22

 

r = (3271 ± 2567.72)/22

 

 

r = 265.4 mph or 32 mph

Since we won't go negative rate heading back... r = 265.4 mph going to

Then r - 77 = 188.4 mph returning

 

Due to rounding and such, these rates are approximate, but come out

good (enough) when plugged into the original equations.