Question

An ostrich can run at a rate of 50 miles in 60 minutes. At this rate, how long would it take an ostrich to run 15 miles?

Answer 1

Hint: We start solving the problem by assigning the variable for the time taken by the ostrich. We then recall the relation between speed, distance, and time as ${\rm{speed}} = \dfrac{{{\rm{distance}}}}{{{\rm{time}}}}$. We will substitute the values in the formula to find the speed of the ostrich. We then find the time required to travel with this speed if the ostrich traveled a distance of 15 miles using ${\rm{time}} = \dfrac{{{\rm{distance}}}}{{{\rm{speed}}}}$.

Complete step-by-step solution:
According to the problem, we are given that an ostrich covers 50 miles in 60 min. We need to find the time required to cover 15 miles if the ostrich travels at the same speed.
Let us assume the time taken is ‘t’ min.
Now, find the speed of the ostrich.
We know that,
${\rm{speed}} = \dfrac{{{\rm{distance}}}}{{{\rm{time}}}}$
Substitute the values in the above formula,
$ \Rightarrow $ Speed $ = \dfrac{{50}}{{60}}$ miles/min
Cancel out the common factor,
$ \Rightarrow $ Speed $ = \dfrac{5}{6}$ miles/min
So, the speed of the ostrich is $\dfrac{5}{6}$ miles/min.
Now, we need to find the time required by the ostrich to travel 15 miles if it travels at a speed of $\dfrac{5}{6}$ miles/min.
We know that,
${\rm{time}} = \dfrac{{{\rm{distance}}}}{{{\rm{speed}}}}$
Substitute the values in the above formula,
$ \Rightarrow t = \dfrac{{15}}{{\dfrac{5}{6}}}$
Move 6 in the numerator,
$ \Rightarrow t = \dfrac{{15 \times 6}}{5}$
Cancel out the common factor,
$ \Rightarrow t = 3 \times 6$
Multiply the terms,
$ \Rightarrow t = 18$ min

Hence, the time taken by an ostrich to run 15 miles is 18 min.

Note: We need to make sure that the units are similar for time, speed, and distance before solving the problem. We should perform every step carefully in order to avoid calculation mistakes. Similarly, we can expect problems to find the percentage difference in the time taken to travel.