Question

Variation

Direct Variation y = kx is equivalent to the statements

y varies directly as x

y is directly proportional to x

Worksheet

1. The number of patients Dr. Wong can see varies directly as the time it takes her to see them. If she can see 11 patients in 3 hours, how long it take her to see 66 patients?

2. The speed of a vehicle varies inversely as the time it takes to travel a fixed distance. If a vehicle travels a fixed distance at 20 miles per hour in 60 minutes, how fast must it travel to cover the same distance in 25 minutes?

Answer 1

Q1.

Number of patients(n) is directly proportional to the time(t) it takes her to see them implies

No of patients seen by doctor in 3 hours is 11 implies

Therefore, the relation becomes

For n=66 implies

Hence, it will take 18 hours for Dr. Wong to see 66 patients

Q2.

Speed is inversely proportional to time it takes to travel a fixed distance implies

For a fixed distance s with speed v=20 mph the value of t=60 min=1 hours implies

Therefore, the relation for v becomes

For the vehicle to travel fixed distance s in 25 minutes implies calculate v for t=25/60=5/12