The total distance between two towns is $80 k m$ . A person covers part of his journey by bike at the rate of $15 k m / h r$ and another part of his journey by bus at $20 k m / r h$ . If the time required for the journey is $4.5$ hours, find the distance covered by each mode of transport.

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Solution

We know that
$D = s \times t$

Time taken by bike jouney $= x$ hours
Time taken by bus jouney $= 4.5 - x$ hours

$\begin{matrix} 15 x + 20 (4.5 - x) = 80 15 x - 20 x + 90 = 80 - 5 x = 80 - 90 x = \frac{- 10}{- 5} = 2 h o u r s \end{matrix}$

Distance covered by bike $= 15 \times 2 = 30 k m$

Distance covered by bus
$\begin{matrix} 20 (4.5 - 2) = 20 \times 2.5 = 50 k m \end{matrix}$

Hence, this is the answer.

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The total distance between two towns is 80 km. A person covers part of his journey by bike at the rate of 15 km/hr and another part of his journey by bus at 20 km/rh. If the time required for the journey is 4.5 hours, find the distance covered by each mode of transport.

We know thatD=s×tTime taken by bike jouney =x hoursTime taken by bus jouney =4.5−x hours15x+20(4.5−x)=8015x−20x+90=80−5x=80−90x=−10−5=2hoursDistance covered by bike =15×2=30 kmDistance covered by bus 20(4.5−2)=20×2.5=50kmHence, this is the answer.

The total distance between two towns is $80 k m$ . A person covers part of his journey by bike at the rate of $15 k m / h r$ and another part of his journey by bus at $20 k m / r h$ . If the time required for the journey is $4.5$ hours, find the distance covered by each mode of transport.