anonymous
  • anonymous
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:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • 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.
anonymous
  • anonymous
any other easy way guys? its too time consuming . This question came for 1 mark and need to solve in 1 minute max.
anonymous
  • anonymous
d=40 km

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anonymous
  • anonymous
ya its 40 km but how? plz solve
anonymous
  • anonymous
\[d=(r+3)\left(t-\frac{40}{60}\right),d=(r-2)\left(t+\frac{40}{60}\right) \]Expand\[d=-2-\frac{2 r}{3}+3 t+r t,d=-\frac{4}{3}+\frac{2 r}{3}-2 t+r t \]
anonymous
  • 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\[\left\{r\to 12,t\to \frac{10}{3}\right\} \]\[r t = 12 \frac{10}{3}=40\text{km}/\text{hr} \]
anonymous
  • 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 \[0=-2-\frac{2 r}{3}+3 t \]
anonymous
  • anonymous
The same simplification holds for the second equation.

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