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?
<pre>Let normal speed be S
Then normal time = {{{150/S}}}
On this day, her speed was: S – 10, and she took {{{150/(S - 10)}}} hours to get to her destination
We then get: {{{150/S = 150/(S - 10) - 30/60}}}________{{{150/S = 150/(S - 10) - 1/2}}}
150(2)(S – 10) = 150(2S) – S(S – 10) --------- Multiplying by LCD, 2S(S – 10)
{{{300S - 3000 = 300S - S^2 + 10S}}}
{{{S^2 - 300S - 10S + 300S - 3000 = 0}}}
{{{S^2 - 10S - 3000 = 0}}}
(S - 60)(S + 50) = 0
Normal speed, or S = {{{highlight_green(60)}}} mph          OR            S  = - 50 (ignore)
Time taken to complete trip: {{{150/(60 - 10)}}}, or {{{150/50}}}, or {{{highlight_green(3)}}} hours