SOLUTION: Rasa drives a bus 150 miles between two connecting cities. During to hazardous road conditions during a recent winter storm, Rasa reduced her rate by 10 mph and safely transported

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Rasa drives a bus 150 miles between two connecting cities. During to hazardous road conditions during a recent winter storm, Rasa reduced her rate by 10 mph and safely transported       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 960627: Rasa drives a bus 150 miles between two connecting cities. During to hazardous road conditions during a recent winter storm, Rasa reduced her rate by 10 mph and safely transported her passengers to their destination 30 minutes later than their scheduled arrival time. What is Rasa’s normal rate of travel? How long did it take for her to complete the trip during the recent storm?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
t, expected time
r, expected speed


________________________speed___________time_________distance
Expected________________r_______________t____________150
Actual__________________r-10____________t+1/2_________150

The question is to find r and t+30.
30 minutes is 1%2F2 hour.

RT=D Uniform Travel Rates Rule.
Setup two equations in r and t, and solve.
system%28rt=150%2C%28r-10%29%28t%2B1%2F2%29=150%29

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Rasa drives a bus 150 miles between two connecting cities. During to hazardous road conditions during a recent winter storm, Rasa reduced her rate by 10 mph and safely transported her passengers to their destination 30 minutes later than their scheduled arrival time. What is Rasa’s normal rate of travel? How long did it take for her to complete the trip during the recent storm?
Let normal speed be S

Then normal time = 150%2FS

On this day, her speed was: S – 10, and she took 150%2F%28S+-+10%29 hours to get to her destination

We then get: 150%2FS+=+150%2F%28S+-+10%29+-+30%2F60________150%2FS+=+150%2F%28S+-+10%29+-+1%2F2

150(2)(S – 10) = 150(2S) – S(S – 10) --------- Multiplying by LCD, 2S(S – 10)

300S+-+3000+=+300S+-+S%5E2+%2B+10S

S%5E2+-+300S+-+10S+%2B+300S+-+3000+=+0

S%5E2+-+10S+-+3000+=+0

(S - 60)(S + 50) = 0

Normal speed, or S = highlight_green%2860%29 mph          OR            S  = - 50 (ignore)

Time taken to complete trip: 150%2F%2860+-+10%29, or 150%2F50, or highlight_green%283%29 hours