Can you help me set up the equations for this word problem p

Can you help me set up the equations for this word problem please? Thank you

At 8:00 am Nancy took off down a river in her boat heading north. Two hours later, William takes off down the same river in his boat also heading north. Nancy\'s boat speed is 3km/hour more than William\'s. At 12:00 pm, Nancy is 44 km ahead of William. What is the speed of each boat?

Solution

Let the speed of Nancy\'s boat be x. Then the speed of William\'s boat is x - 3. At 12.00 pm ( i.e. mid-day), Nancy has been travelling for 4 hours and William has been travelling for 2 hours.

The distance travelled by Nancy\'s boat in 4 hours is 4x . ( distance = speed * time)

The distance travelled by William\'s boat in 2 hours is 2(x -3)

Since both the boats are heading in the same direction ( North) and since the distance between the two boats at 12.00 pm is 44 km, we have 4x - 2 (x -3) = 44 or, 4x - 2x + 6 = 44 or, 2x = 44 - 6 = 38. Therefore x = 38/2 = 19 and x - 3 = 19 - 3 = 16. Thus, Nancy\'s boat is travelling at 19 kph and the speed of William\'s boat is 16 kph.