Atourist has planned a trip to cover the distance of 640 miles, driving at some constant speed. however, when he already covered a quarter of the distance, he took a rest for 1.2 hours. then, in order to arrive at the destination on time, he increased the speed by 20 mph. how long, actually, the trip lasted?

The trip lasted for a total of 8 hours.

Step-by-step explanation:

Distance planned = S = 640 miles

Constant speed = V

Thus the time to be taken would be = T = V/S

We have an equation 640 = VT ----- eq (a)

Time For First Quarter = T/4

speed = V

Distance = 640/4 = 160

After first quarter, there is a rest of 1.2 hours and to complete his trip on time, he increased the velocity by 20 mph.

So, the remaining distance = 640 - 160 = 480 miles.

Speed = V + 20 mph

Time remaining = [(T-T/4) - 1.2] = 3T/4 - 1.2 hours

We have an equation for remaining distance s = vt

=> 480 = (V+20)(3T/4 - 1.2) ----- eq (b)

using eq (a), we have V = 640/T. Putting it in eq (b), we have:

Solving the equation, we get T = 8 or T = -32/5(which is not possible.

So, the right answer is T = 8 hours