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?

  168 km

Step-by-step 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

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step-by-step explanation: