Question

A boy travels a distance of $25\mathrm{km}$ in 4 hours partly on foot at rate $3.5\mathrm{km}/\mathrm{h}$ and partly on cycle at $9\mathrm{km}/\mathrm{h}$. Find the distance on foot and on cycle.

• A. $7\mathrm{km}$
• B. $2\mathrm{km}$
• C. $6\mathrm{km}$
• D. $18\mathrm{km}$

Answer 1

Answer: (A), (D)

Let distance by foot is $\mathrm{X}\mathrm{km}$ in $t$ hours By cycle is $25-\mathrm{X}\mathrm{km}$ in $4-\mathrm{t}$ hours
$\text{ Distance }=\text{ speed }\times \text{ time }$
$\Rightarrow \mathrm{X}=3.5\times t$
$\Rightarrow 25-x=9\times (1-t)$
$\Rightarrow 25-3.5t=36-9t$
$\Rightarrow 5.5\mathrm{t}=11$
$t=2$
$X=3.5\times 2=7\mathrm{km}\text{ (Distance by foot) }$
$\text{ By cycle }=25-x\text{ in }4-\mathrm{t}\text{ hours }$
$\Rightarrow 4-2=2\text{ hours }$
$\Rightarrow 25-x=25-7$
$=18\mathrm{km}\text{ (Distance by cycle) }$