Question 227726
When traveling to work each day, John drives part of it on the highway (where he goes 65 mph) and the rest on a ranch road (where he can only go 42 mph). The trip is 13.95 miles, and it takes only 15 minutes (which is 1/4 hour , or 0.25 hours). What part of an hour does he spend driving on each type of road?


Step 1.  Let t be the time (in hours) traveled on the highway.


Step 2.  Let 65t be the distance traveled on the highway.


Step 3.  Let 0.25-t be the time traveled (in hours) on the ranch road.


Step 4.  Let 42(.25-t) be the distance traveled on the ranch road.


Step 5.  Then 13.95=65t+42(0.25-t)=10.5+23t since the total distance is 13.95 miles.


Step 6.  Solving yields the following steps


{{{13.95=10.5+23t}}}


Subtract 10.5 from both sides of the equation


{{{13.95-10.5=10.5+23t-10.5}}}


{{{3.45=23t}}}


Divide by 23 to both sides of the equation


{{{3.45/23=23t/23}}}


{{{t=0.15}}} hour and {{{0.25-t=0.10}}} hour


Check distance traveled 65*0.15+42*0.10=9.75+4.2=13.95 which is  a true statement.


Step 7.  ANSWER:  John spent 0.15 hour on the highway and 0.10 hour on the ranch road.


I hope the above steps were helpful.


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Respectfully,
Dr J

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