The circumference of the front wheel of a cart is 40 ft long and that of the back wheel is 48 ft long. What is the distance travelled by the cart, when the front wheel has done five more revolutions than the rear wheel?

### Concept & Strategy Both wheels travel the exact same linear distance ($D$). $$\text{Revolutions} = \frac{\text{Distance}}{\text{Circumference}}$$ Set up an equation equating the difference in revolutions between the front and rear wheels to 5. ### Step-by-Step Solution * **Given:** * Front wheel circumference ($C_1$) = $40\text{ ft}$ * Back wheel circumference ($C_2$) = $48\text{ ft}$ * Let the total distance travelled be $D\text{ ft}$. * **Express the number of revolutions:** $$\text{Front wheel revolutions } (n_1) = \frac{D}{40}$$ $$\text{Rear wheel revolutions } (n_2) = \frac{D}{48}$$ * **Formulate the equation:** $$\frac{D}{40} - \frac{D}{48} = 5$$ * **Solve for $D$:** $$\text{LCM}(40, 48) = 240$$ $$\frac{6D - 5D}{240} = 5$$ $$\frac{D}{240} = 5$$ $$D = 5 \times 240 = 1200\text{ ft}$$ ### Exam Strategy & Shortcut Formula for distance when difference in revolutions is $\Delta n$: $$D = \frac{C_1 \times C_2}{C_2 - C_1} \times \Delta n = \frac{40 \times 48}{48 - 40} \times 5 = \frac{1920}{8} \times 5 = 240 \times 5 = 1200\text{ ft}$$ ### Common Pitfall Setting $\frac{D}{48} - \frac{D}{40} = 5$, which results in a negative value because the smaller wheel makes more revolutions. ### Final Answer Therefore, the correct answer is **1200 ft**.