Chapter 6.2, Problem 27HP

To determine

To find: The situation in which the rate $\frac{x\text{miles}}{y\text{hours}}$ decreases out of given following two conditions: (i) x increases , y is unchanged (ii) x is unchanged, y increases

Answer to Problem 27HP

The rate $\frac{x\text{miles}}{y\text{hours}}$ decreases in second condition when x is unchanged, y increases. For example, if a driver stays on a hotel for a cup of tea etc, even distance covered from initial point remains the same but time goes on increasing and accordingly his overall speed of the journey decreases.

Explanation of Solution

Given information: Given a ratio $\frac{x\text{miles}}{y\text{hours}}$ and two conditions to be applied on this ratio:

(i) x increases , y is unchanged (ii) x is unchanged, y increases

Concept used:Value of a fraction, when its numerator is greater than is denominator is always more than the value of a fraction with greater denominator.

Calculation: In first condition, x increases , y is unchanged , the numerator of given ratio will be greater than the denominator and in second condition when x is unchanged, y increases, the value of the ratio will less than the original value given, based on above concept. So, clearly the fraction of first condition will give greater value than the value of fraction in second condition.

Conclusion: Based on above fact, rate of given ratio will decrease in second case i.e. when x is unchanged, y increases.