Please answer the question below with instructions

Question

Julie recently drove to visit her parents who 240 live miles away. On her way there her average speed was 25 miles per hour faster than on her way home (she ran into some bad weather). If Julie spent a total of 8 hours driving, find the two rates.

Answer 1

R is the slower speed

T is the faster time

240 = (r+25)* T <--- driving to parents

= r*(8-t) <--- return trip

rT + 25T = 8r - rT <--- distributive property

2rt + 25t = 8r

t( 2r + 25) = 8r

t = (8r)/(2r + 25) <--- saves this equation for later

240 = (r+25)(8r)/(2r + 25) <--- plugs into first equation

(2r+25)(240) = (8r)(r+25) <-- cross multiplication

(2r+25)(30) = r(r+25) <---- divides both sides by 8

60r + 750 = r^2 + 25r <---- distributive again

0 = r^2 - 35r - 750 <--- moves everything from left to right

0 = ( r - 50 )(r + 15 ) <--- factors

r + 15 = 0 ---.> r=-15 DISQUALIFIED... negative speed not allowed

r-50 = 0 --- r = 50

Then per the equation above in bold,

t = (8*50)/(2 * 50 + 25) = 400/125 = 16/5 = 3 and 1/5 hours = 3 hours and 12 minutes

She drives TO her parents at a speed of 75 mph for 240/75 = 3.2 hours = 3 hours and 12 minutes

She drive FROM her parents at a speed of 50 mph for 240/50 = 24/5 = 4.8 hours = 4 hours and 48 min