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Jimmy drove to his cabin on the lake and back. it took 0.6 hours longer to go there than it did to come back. the average speed on the trip there was 46 km/h. the average speed on the way back was 52 km/h. how many hours did the trip there take

Respuesta :

BlueSky06
To answer this item, we let x be the distance that Jimmy drove from his origin and back. Given the speeds, the time it takes for him to travel to and fro are,
                                   t1 = x / 46
                                   t2 = x / 52
respectively.

The equation that would best represent the scenario is,
                              x/46 - x/52 = 0.6
The value of x from the equation is 239.2.

The trip there takes x/46 which is equal to 239.2/46 which is also equal to 5.2 hours. The travel from the cabin back took 4.6 hours. 

Answer:

9.8 hours

Step-by-step explanation:

Let the distance be x km

T1 be time taken to go to trip

T2 be time taken to go back trip

Time = [tex]\frac{distance}{speed}[/tex]

Average speed on way of trip = 46 km/h

T1 = [tex]\frac{x}{46}[/tex]

Average speed on the way back = 52 km/h

T2 = [tex]\frac{x}{52}[/tex]

According to question

T1-T2 = 0.6

[tex]\frac{x}{46}[/tex]-[tex]\frac{x}{56}[/tex]= 0.6

[tex]\frac{26x-23x}{1196}[/tex]=0.6

3x=1196×0.6

3x=717.6

x=[tex]\frac{317.6}{2}[/tex]

x=239.2 km

T1=[tex]\frac{239.6}{46}[/tex]

T1=5.2 hour

T2=[tex]\frac{239.6}{52}[/tex]

T2=4.6 hour

Total time taken to complete the trip = T1+T2

Total time = 5.2+4.6 =9.8

Hence the correct answer is 9.8 hours

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