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A business executive travels 1120 miles in a corporate jet and then travels an addtional 60 miles by car. The plane ride took two hours longer than the car ride. The jet travels 8 times the speed of the car. Find the total time for the 1180 mile trip.

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[Problem Statement]

A business executive travels a total distance of 1180 miles, comprised of:

- 1120 miles by corporate jet

- 60 additional miles by car

It is given that:

- The jet ride takes 2 hours longer than the car ride

- The jet travels at a rate 8 times the speed of the car

[Comprehensive Step-by-Step Working]

Let:

- J = Speed of the jet (in miles/hour)

- C = Speed of the car (in miles/hour)

- TJ = Time taken for jet ride (in hours)

- TC = Time taken for car ride (in hours)

- D = Total distance traveled = 1120 + 60 = 1180 miles

As per the question,

- J = 8C (Jet speed is 8 times car speed)

- TJ = TC + 2 (Jet ride is 2 hours longer than car ride)

Using speed-time-distance formula:

- Distance = Speed x Time

For jet ride:

- 1120 miles = J x TJ

- 1120 miles = J x (TC + 2) [Substituting TJ]

- 1120 miles = 8C x (TC + 2) [Substituting J = 8C]

For car ride:

- 60 miles = C x TC

[Solution]

Solving the above two equations simultaneously:

- TC = 6 hours

- TJ = TC + 2 = 6 + 2 = 8 hours

Therefore, the total travel time for the 1180 mile trip is 8 hours.

User Mocherfaoui
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