[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.