Question 230314
The average speed of a moving van is 24 km/h faster than that of a delivery truck. If the van travels the same distance in 5h as the truck travels in 7 h, find the average speed of each.


Step 1.  Let x be the speed of the delivery truck


Step 2.  Let x+24 be the speed of the moving van since it travels 12 km/h faster than the truck.


Step 3.  We note that distance=speed*time.


Step 4   Let 7x be the distance traveled by the delivery truck for 7 hours.


Step 5.  Let 5(x+24) be the distance traveled by the moving van for 5 hours.


Step 6.  Step the expressions in Steps 4 and 5 to be equal since the distance traveled by the truck and van are equal.


{{{5(x+24)=7x}}}


Step 7.  Solving yields the following steps


{{{5x+120=7x}}}


Subtract 5x from both sides of the equation


{{{5x+120-5x=7x-5x}}}


{{{120=2x}}}


Divide by 2 to both sides of the equation


{{{120/2=2x/2}}}


{{{x=60}}} and {{{x+24=84}}}.


Check if the distances are the same


{{{7*60=5*84}}}


{{{420=420}}} which is a true statment.


Step 7.  ANSWER:  The delivery truck is traveling at 60 km/hr and the moving van is traveling at 84 km/hr.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J