Many real life problems can be solved using rational equations.

• Business situations concerning average revenue or average cost.
• Distance-time-velocity problems.
• Concentration conversions in chemistry.
• Work related situations involving productivity rates.

Judy and Greg have a large property to maintain. They usually work together to mow their lawn; Judy uses the riding mower and Greg the push mower. Together, it takes them \(45\) minutes to mow the lawn. On her own, Judy can mow the lawn in \(1\) hour with the riding mower. How long would it take Greg to mow the lawn on his own, using the push mower?

Solution

To solve this problem, let \(t\) represent the time, in minutes, it takes Greg to mow the lawn on his own.

• Judy works at a rate of \(\dfrac{1}{60}\) of a lawn per minute.
• Greg works at \(\dfrac{1}{t}\) of a lawn per minute.
• Together, Judy and Greg mow \(1\) lawn in \(45\) minutes, so they work at a rate of \(\dfrac{1}{45}\) of a lawn per minute.

Therefore,

Thus \(t=180\), which satisfies the condition, \(t \gt 0\).

Therefore, it would take Greg \(3\) hours \(\left( 180 \right.\) minutes\(\left. \right)\) to cut the lawn on his own, using the push mower.