Question

How much time will it take a car traveling at \[\text{88 km/hr}\left( \text{55 mi/hr} \right)\] to travel \[\text{500 km}\] ?

Answer 1

Hint: In this question, we have to find the time taken by the car to travel $\text{500 km}$ with a speed of $\text{88 km/hr}$ . So, we apply distance- speed formula, to get our required answer. After applying the formula, divide both sides by 88, and after necessary calculations get the value of time taken by the car, which is our required answer.

Complete step by step answer:
According to the question, we have to find the time taken by the car.
Let the distance traveled by car is denoted by D = $\text{500 km}$. --- (1)
Let the speed of the car be S = $\text{88 km/hr}$. -------- (2)
In addition, let the time taken by the car be T = x hrs --------- (3)
Now, we apply the distance-speed formula, that is $\text{distance = speed }\text{. time}$ ------- (4)
Let us substitute the values (1), (2), and (3) in equation (4), we get
$\begin{align}
  & \Rightarrow \text{D = S}\text{. }x \\
 & \Rightarrow \text{500= 88}\text{. }x \\
 & \\
\end{align}$
Now, we will divide both sides by 88 on the above equation, we get
\[\Rightarrow \dfrac{500}{88}=\dfrac{88.x}{88}\]
As we know, the same terms will cancel out in the division, thus we get
$\Rightarrow \dfrac{500}{88}=x$
$\Rightarrow x\text{=5}\text{.681}$
Therefore, the time taken by the car to travel $\text{500 km}$ with a speed of $\text{88 km/hr}$ is $5.681\text{ hrs}$ .

Note: We should perform all the steps carefully to avoid any confusion, especially in the distance-speed formula. Always keep in mind that the distance is the product of speed and time. One of the alternative methods is that we can change the units of the terms and perform the same steps to get the required answer.
An alternative method:
1 km= 0.621371 miles
1 km/hr= 0.621371 miles/hr
Let the distance traveled by car is denoted by D = $\text{500 km= 310}\text{.686 miles}$ --- (5)
Let the speed of the car be S = $\text{88 km/hr= 54}\text{.6807 miles/hrs}$. -------- (6)
And, let the time taken by the car be T = x hrs --------- (7)
Now, we apply the distance-speed formula, that is $\text{distance = speed }\text{. time}$ ------- (8)
Let us substitute the values (5), (6), and (7) in equation (8), we get
$\begin{align}
  & \Rightarrow \text{D = S}\text{. T} \\
 & \Rightarrow 310.686\text{= 54}\text{.6807 }\text{. }x \\
\end{align}$
Now, we will divide both sides by 54.6807 on the above equation, we get
\[\Rightarrow \dfrac{310.686}{54.6807}=\dfrac{54.6807.x}{54.6807}\]
As we know, the same terms will cancel out in the division, thus we get
$\Rightarrow \dfrac{310.686}{54.6807}=x$
$\Rightarrow x\text{=5}\text{.681}$
Therefore, the time taken by the car to travel 310.686 miles with a speed of 54.6807 miles/hr is $5.681\text{ hrs}$ .