anonymous 5 years ago A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is:

1. anonymous

vt=d (v+3)(t-2/3)=d (v-2)(t+2/3)=d 3 equations and three unknowns so you can find d.

2. anonymous

any other easy way guys? its too time consuming . This question came for 1 mark and need to solve in 1 minute max.

3. anonymous

d=40 km

4. anonymous

ya its 40 km but how? plz solve

5. anonymous

$d=(r+3)\left(t-\frac{40}{60}\right),d=(r-2)\left(t+\frac{40}{60}\right)$Expand$d=-2-\frac{2 r}{3}+3 t+r t,d=-\frac{4}{3}+\frac{2 r}{3}-2 t+r t$

6. anonymous

Solve the following simultaneous equations for r and t.$0=-2-\frac{2 r}{3}+3 t,0=-\frac{4}{3}+\frac{2 r}{3}-2 t$ I got$\left\{r\to 12,t\to \frac{10}{3}\right\}$$r t = 12 \frac{10}{3}=40\text{km}/\text{hr}$

7. anonymous

Note: r t = d$d=-2-\frac{2 r}{3}+3 t+r t$simplifies to$d=-2-\frac{2 r}{3}+3 t+d$subtracting d from each side $0=-2-\frac{2 r}{3}+3 t$

8. anonymous

The same simplification holds for the second equation.