Question

A car at 7:30AM is moving at a constant speed of $4\,km{\min ^{ - 1}}$ and an odometer reading recorded is $28568\,Km$ . What would be the odometer reading at $9:15\,am$ ?
(A) $28673\,km$
(B) $28988\,km$
(C) $29255\,km$
(D) $28568\,km$

Answer 1

Hint: From the given time, calculate the time interval between these two time periods. Use the formula of the distance to find the distance covered during the time period. Add the obtained answer with the old given odometer reading to find the new odometer reading.
Formula used:
The formula of the distance is given by
$d = st$
Where $d$ is the distance travelled by the car, $s$ is the speed of the car and the $t$ is the time taken.

Complete answer:
It is given that at $7:30\,am$ , the car moves with the constant speed $4\,km{\min ^{ - 1}}$ and the reading of the odometer is $4\,km{\min ^{ - 1}}$ .
The time interval between the odometer reading from $7:30\,am$ to $9:15\,am$ is $1$ hour and $45$ minutes.
The $1$ hour and $45$ minutes time period is converted into minutes in the following way.
$1\,hr = 60\,\min $
$1$ hour and $45$ minutes $ = 60 + 45 = 105\,\min $
Hence the time taken at $9:15\,am$ is $105$ minutes.
Let us use the formula of the distance,
$d = st$
Since the speed of the car is same till $9:15\,am$, substitute the speed and the time taken by the car in the formula of the distance, we get
$
  d = 4 \times 105 \\
  d = 420\,km \\
 $
Hence the distance travelled by the car between the time period of $7:30\,am$ and the $9:15\,am$ is calculated as $420\,km$. In order to calculate the total distance covered by the car up to $9:15\,am$ , the distance covered by the car before the time $7:30\,am$ and the distance between the time period of $7:30\,am$ and the $9:15\,am$ is added.
$
  {\text{odometer}}\,{\text{reading}}\,9:15\,am = 28568 + 420 \\
= 28988\,km \\
 $
Hence the odometer reading at the time $9:15\,am$ is obtained as $28988\,km$ .

Thus the option (B) is correct.

Note:
The odometer is the device used to measure the distance covered by the vehicle. It is placed in the dashboard of the vehicle. In the above solution, it is given as constant speed, so the same speed is substituted for finding the distance covered in the time period between the given two times.