Question

Ajit can ride a scooter constantly at a speed of 30km/hour. Draw a time-distance graph for this situation. Use it to find. (i) the time taken by Ajit to ride 75km. (ii) the distance covered by Ajit in 7/2 hours.

Answer 1

$\sf\fbox{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:Answer\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}$

$\bold\pink{Given}$

$\sf{Speed\: of \:scooter = 30\:km/hour}$

$\bold\pink{To\: find. }$

$\sf{(i)\: The \:time \:taken \:by\: Ajit \:to \:ride \:75\:km}$

$\sf{(ii)\: The\: distance \:covered \:by \:Ajit\: in\: 7/2 \:hours}$

$\bold\pink{Concept:}$

$\sf{The \:formula\: for \:distance\: is:}$ $\small\underline{\boxed{\sf\;\;Distance = Speed \times Time}}$

$\bold\pink{Solution:}$

$\sf{We\: need\: to \:make \:a\: \:time-distance\: graph}$

$\sf{So,}$

$\sf{Finding \:different\: values\: of \:distance\: at \:}$ $\sf{different\:values\: of \:time}$

$\tiny\boxed{\begin{array}{cc} \: \sf Time & \sf Distance \\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}& \\\sf 1\:hour&\sf 30 \times 1 =30\:km \\\ \\ \sf 2\:hours &\sf 30 \times 2 =60\:k.m \\\ \\ \sf 3\:hours &\sf 30 \times 3 =90\:k.m \\\ \\ \sf 4\:hours &\sf 30 \times 4 =120\:k.m &\sf \end{array}}$

$\sf{We\:get\:the\: values\:as:}$

$\tiny\boxed{\begin{array}{cc} \: \sf Time\:(in\:hours) & \sf Distance\:(in\:km) \\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}& \\\sf 1&\sf 30 \\\ \\ \sf 2 &\sf 60 \\\ \\ \sf 3 &\sf 90\\\ \\ \sf 4 &\sf 120 &\sf \end{array}}$

$\bold\pink{ANSWER\: (i)}$

For graph see the first attachment

$\sf{Corresponding \: to \: 75 \: km \: on \: the \: y-axis, }$ $\sf{we \: get\:the \: time \: to \: be \: 2.5 \: hours \: on \: the \: }$ $\sf{x-axis. \: Thus \: 2.5 \:hours \: are \: needed \: to \: cover}$ $\sf{75 \:km}$

$\bold\pink{ANSWER \:(ii)}$

For graph see the second attachment

$\sf{Corresponding \: to\: \frac{7}{2} \: hours \: on \: the \: x-axis,}$ $\sf{ the \: distance \: covered \: is \: 105 \: km \: on \: the}$ $\sf{ y-axis}$