## Predicting Values

#### Predicting Values from Direct or Inverse Variations

Once we know the functional dependency of one variable with another, i.e. it varies directly or inversely, we can
easily use the variation model to predict future values of a function.

Let us understand using the following example.

James when driving at a speed of 30 km/hr reaches his office in 1.5 hours. Find the time he would take to reach his
office if he travels at a speed of 45 km/hr.

Solution

In each case, James travels the same distance but with a different speed.

We also know the relation between speed, time and distance, i.e. distance = speed x time or time = distance/speed.

When distance is constant, then times varies inversely with speed.

It is given that when the speed = 30km/hr then the time taken is 1.5 hrs.

The distance travelled by James = 30 x 1.5 = 45 km.

Using the inverse relation between time and speed, time = distance/speed = 45/45 = 1.

Hence with a speed of 45km/hr, James will reach his office in 1 hour.

#### Try this problem

1.     Laura bought her first car and drove at a speed of 90 km/hr in 2 hours to reach the city. She turned up late for
her meeting. How sooner would she have reached the city had she traveled at a speed of 120 km/hr on the
highway?

Explanation: When distance is constant, time becomes inversely related to speed.

Given that her speed was 90 km/hr and her travel time was 2 hours, the distance she traveled was:

90km/hr x 2 hrs = 180 km.

Using the inverse relation between time and speed, we find the time:

Distance / speed = 180 km / 120 km/hr
= 1.5 hrs

How sooner she would have reached the city:

2 hours – 1.5 hours = 0.5 hours or 30 minutes sooner