<PRE><B>Question 331739</B>
Domic rode his motorbike 20 min to Helen’s home, 
and then the two drove in a car 30 min to the beach 35 mi from Dominic’s home.
 If the car speed was 10 mi/h faster than that of the motorbike, how fast did the car travel?
:
A rough diagram will make it look simple
:
D----------20 min-----------H------------30 min-----------Beach
|------------------------------35 mi------------------------|

Let s = motorcycle speed
then
(s+10) = car speed
:
Change 20 min to 1/3 hr
Change 30 min to 1/2 hr
Write a dist equation, Dist = time * speed
:
motorcycle dist + car dist = 35 mi
{{{1/3}}}s + {{{1/2}}}(s+10) = 35
multiply by 6 to get rid of the denominators, results:
2s + 3(s+10) = 6(35)
2s + 3s + 30 = 210
5s = 210 - 30
5s = 180
s = {{{180/5}}}
s = 36 mph is the motorcycle
then
36 + 10 = 46 mph is the car
:
:
Check solutions using the distances
{{{1/3}}}(36) + {{{1/2}}}(46) =
12 + 23 = 35 mi; confirms our solutions

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