Traveling at a constant rate of 15 miles per hour, it took Bob x hours

Using logic, we know that in second case, Bob travelled 1 hr less because he travelled 5 miles extra for each of the (x - 1) hrs. This is the distance he would have covered in the last hour in the first case.

5*(x - 1) = 15
x = 4

Answer (C)

Let the distance travelled be 60 miles (LCM of 15 & 20)

So, Travelling at 15 miles/hour time taken is 4 hours & Travelling at 20 miles/hour time taken is 3 hours

Thus, the value of x is 4, Answer must be (C) 4

When I first saw these types of questions I could answer the simple ones, but was still confused by the units. I'm putting the below for others in similar situations.

1st trip \(\frac{15(miles)}{1(hour)}·x(hours)=distance\)

2nd trip \(\frac{20(miles)}{1(hour)}·(x-1)(hours)=distance\)

The distance is the same in both so we can have the equations equal each other

\(\frac{15(miles)}{1(hour)}·x(hours)=\frac{20(miles)}{1(hour)}·(x-1)(hours)\)

Simplification: Each side has hours in the denominator and numerator so they can be cancelled from each side. Just remember that we're trying to find x and it uses the unit hours

\(\frac{15(miles)}{1}·x=\frac{20(miles)}{1}·(x-1)\)

Simplification: Both sides of the equation use the unit miles, so it can be cancelled from both sides of the equation.

\(\frac{15}{1}·x=\frac{20}{1}·(x-1)\)

15x=20x-20
0=5x-20
0=x-4
4=x