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.

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?**Answer:****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 hrsHow sooner she would have reached the city:

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

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