Question

Mike drove \[30miles\], at a constant speed, for \[t\] hours and then drove \[y\] miles, at another speed, for \[1\] hour and \[15\] minutes. What was his average speed, in miles per hour, for the whole journey?
A. \[\dfrac{{\left( {\dfrac{{30}}{t} + \dfrac{y}{{1.25}}} \right)}}{2}\]
B. \[\dfrac{{\left( {30 + y} \right)}}{{\left( {t + 1.25} \right)}}\]
C. \[\dfrac{{\left( {30 + y} \right)}}{t}\]
D. \[\dfrac{{\left( {30 + y} \right)}}{{2\left( {t + 1.25} \right)}}\]

Answer 1

Hint: We all know that speed is the measure of how briskly an object moves with respect to some other object. There are two styles of speed namely instantaneous speed and also average speed. The average speed of an object will be termed as the total distance traveled by it in an exceedingly particular interval of time. It can be calculated by dividing the overall distance traveled by the total time taken.

Formula used:
Speed, \[s = \dfrac{d}{t}\]
Where, $d = $ Distance and $t = $time.
If ${d_1}$ distance covered in time ${t_1}$ and ${d_2}$ distance covered in time ${t_2}$
Average speed \[ = \dfrac{{{d_1} + {d_2}}}{{{t_1} + {t_2}}}\]

Complete step by step answer:
Journey 1: \[30miles\] at a constant speed for \[t\] hours, ${d_1} = 30$ and ${t_1} = t$
Journey 2: \[y\] miles at another speed for \[1\] hour \[15\] minutes.${d_2} = y$
\[{t_2} = \]\[1\] hour \[15\] minutes
\[\Rightarrow {t_2}\] = \[75\] minutes
\[\Rightarrow {t_2}\] = \[\dfrac{{75}}{{60}}\,hour \]
\[\Rightarrow {t_2} = 1.25\,hour\]
Average speed \[ = \dfrac{{{d_1} + {d_2}}}{{{t_1} + {t_2}}}\]
Average speed \[ = \dfrac{{\left( {30 + y} \right)}}{{(t + 1.25)}}\].

Hence, option B is correct.

Additional information: Speed may be a scalar quantity that has only magnitude and not direction. We all know that speed is a change within the distance with respect to time. This suggests that if the speed of the object is high, then it’s moving fast, whereas if the speed of the object is low, then it’s moving slowly. Clearly, speed depends on time.

Note: Both velocity and speed measure how briskly an object moves. But there’s a small difference between velocity and speed. Velocity could be a vector quantity that has both direction and magnitude, unlike speed which could be a scalar quantity and might have only magnitude and not direction. This is often one major difference between them both, and it’s a physical quantity.