Question

When visiting his parents, Tyler drives at an average speed of 42 km/h through urban areas and at an average speed of 105 km/h on the motorway. His journey usually takes him 2.5 hours. One day when there is fog, he sets off 1 hour early and only manages to drive at an average speed of 28 km/h in the urban areas and 60 km/h on the motorway. He arrives 30 minutes late. What was the total distance that Tyler travelled?

Answer 1

168 km

Explanation:

Let x represent the distance Tyler drives at the slower speed, and let y represent the distance at the higher speed. Using time = distance/speed, we can write equations for the total travel time:

x/42 +y/105 = 2.5

x/28 +y/60 = 4.0 . . . . . 1.5 hours more than the usual 2.5 hours

Multiplying the first equation by 210, we have ...

5x +2y = 525

Multiplying the second equation by 420, we get ...

15x +7y = 1680

Subtracting 3 times the first of these equations from the second, we have ...

(15x +7y) -3(5x +2y) = (1680) -3(525)

y = 105

Putting this into the very first equation, we get ...

x/42 + 105/105 = 2.5

x/42 = 1.5 . . . . . . subtract 1

x = 63 . . . . . . . . .multiply by 42.

The total distance to Tyler's parents' house is ...

63 km + 105 km = 168 km