Subtracting 20 from each side gives us3 x= 180Dividing through by 3, we getx= 60That means Bonnie weighs 60 kg. Bruce weighs 5 kg more than Bonnie, or 65 kg. Bill
weighs 10 kg more than Bruce, or 75 kg.- We can work through this without resorting to equations. It’s first-degree algebra in a
single variable, but we don’t have to express it symbolically! Let’s start by figuring out
the land speed of the boat as it traveled upstream. The distance from our cabin to our
cousin’s cabin is 18 miles (mi), and it took 1 h 12 min for the boat to travel that far.
Because 12 min = 1/5 h, the trip took 6/5 h. The speed of the boat relative to the land
was therefore 18 mi per 6/5 h, or
18/(6/5)= 18 × 5/6
= 15 mi/hIf there were no current, the boat would have traveled at 18 mi/h relative to the water and
relative to the land. The water speed was indeed 18 mi/h, but the land speed was only
15 mi/h. The current slowed our boat down by 18 − 15, or 3 mi/h. The river must there-
fore have been flowing at 3 mi/h.- When we go downstream, the river current will add 3 mi/h to our boat’s land speed.
Again, if there were no current, the land and water speeds would both be 18 mi/h. That
means the downstream speed of the boat will be 18 + 3, or 21 mi/h. We must travel
a land distance of 18 mi. Time equals distance divided by speed. Therefore, if we let t
represent the time in hours, we have
t= 18/21
= 6/7 hBecause 1 h = 60 min, 6/7 hour = 6/7 × 60 min, or, approximately, 51.43 min.Chapter 13
- For every boy there is exactly one girl dance partner and vice-versa, so the mapping is an
injection. It’s also onto the entire set of girls. No girl has to sit out the dance without a
partner, so it’s a surjection. Any mapping that’s both an injection and a surjection is, by
definition, a bijection. - This mapping is not one-to-one, so it’s not an injection. That means it can’t be a
bijection. However, it’s a surjection, because it’s onto the entire set of girls.
Chapter 13 627