A driver took a day-trip at two different speeds. He drove 100 miles at a slower speed and 240 miles at a speed 10 miles per hour faster. If the time spent during the faster speed was twice that spent at a slower speed, find the two speeds during the trip

So, time faster = 2 · time slower;

We have formula: time slower = 100 / slower speed;

time faster = 240 / (10 + slower speed);

Then, 240 / (10 + slower speed) = 2 · (100 / slower speed);

Let slower speed be x;

We solve the equation: 240 / (10 + x) = 2 · (100 / x);

240 / (10 + x) = 200 / x;

240x = 200 (10 + x);

240x = 2000 + 200x;

40x = 2000;

x = 50 miles per hour (the slower speed);

The faster speed: 50 + 10 = 60 miles per hour.