SOLUTION: A bus traveled on a straight road for 2 h at an average speed that was 20 mph faster than its average speed on a winding road. The time spent on the winding road was 3 h. Find the

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Question 1048489: A bus traveled on a straight road for 2 h at an average speed that was 20 mph faster than its average speed on a winding road. The time spent on the winding road was 3 h. Find the average speed on the winding road if the total trip was 250 mi.
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39632) About Me  (Show Source):
You can put this solution on YOUR website!
Travel Rates Rule for constant rate, RT=D relates rate, time, distance. 

                    RATE       TIME      DISTANCE
STRAIGHT            r+20        2
WINDING             r           3
Total                                     250

Use the basic rule to fill the missing information in the table. 
                    RATE       TIME      DISTANCE
STRAIGHT            r+20        2        %28r%2B20%29%2A2
WINDING             r           3        %28r%29%283%29
Total                                     250


There is a sum to give you an equation, for the distance.

%28r%2B20%29%2A2%2B3r=250
and as formulated here, the question asks for a solution of r.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = distance in miles traveled on
the straight road
+250+-+d+ = distance in miles traveled on the
winding road
Let +s+ = speed in mi/hr on winding road
+s+%2B+20+ = speed in mi/hr on straight road
-------------------------------------------
Equation for straight road:
(1) +d+=+%28+s%2B20+%29%2A2+
Equation for winding road:
(2) +250+-+d+=+s%2A3+
--------------------------
Substitute (1) into (2)
(2) +250+-+2s+-+40+=+s%2A3+
(2) +5s+=+210+
(2) +s+=+42+
The speed on the winding road was 42 mi/hr
-----------------
check:
(1) +d+=+%28+42+%2B+20+%29%2A2+
(1) +d+=+124+ mi
and
(2) +250+-+d+=+3%2A42+
(2) +d+=+250+-+126+
(2) +d+=+124+ mi
OK