Chapter 7.8, Problem 4ST

To determine

To find: the time at which main engine and reserve engine both run together.

Answer to Problem 4ST

The $\text{34}\frac{\text{2}}{\text{7}}$ seconds both rockets are on and can run at same time.

Explanation of Solution

Given:

The main engine on a rocket can use up the fuel in $\text{60sec}$.

The reserve engine can use it up in $\text{80sec}$.

Concept used:

Fraction can be solved by taking L.C.M.

The equation will be:

  $\frac{\text{x}}{\text{60}}\text{+}\frac{\text{x}}{\text{80}}\text{=1}$.

Calculation:

According to the given data:

The main engine on a rocket can use up the fuel in $\text{60sec}$.

The reserve engine can use it up in $\text{80sec}$.

Let $\text{x}$ be the number of seconds both rockets are on.

The equation will be:

  $\frac{\text{x}}{\text{60}}\text{+}\frac{\text{x}}{\text{80}}\text{=1}$.

By solving the fraction using L.C.M:

  $\frac{\text{7x}}{\text{240}}\text{=1}$.

Dividing both side by $\frac{7}{240}$ :

  $\text{x=}\frac{\text{240}}{\text{7}}\text{ or x=34}\frac{\text{2}}{\text{7}}$.

Hence the $\text{34}\frac{\text{2}}{\text{7}}$ seconds both rockets are on and can run at same time.