Question

Joshua traveled 5 hours from City A to City B. The distance between the cities is 260 miles. First he traveled at the constant speed of 40 mi/h, and then at the constant speed of 60 mi/h. How many hours did he travel at the constant speed of 60 mi/h?

Answer 1

Joshua  travelled for 3 hours at the constant speed of 60 mi/h

Solution:

Given that, Joshua traveled 5 hours from City A to City B

The distance between the cities is 260 miles.  

First he traveled at the constant speed of 40 mi/h, and then at the constant speed of 60 mi/h.  

So, let the number of hours he travelled with 40 mi/h be "n" hours and the distance travelled be "x" miles

Then, the time in which he travelled with 60 mi/h will be 5 – n hours and distance travelled will be 260 – x miles

We have to find how many hours did he travel at the constant speed of 60 mi/h

The relation between speed and distance is given as:

$\text { distance }=\text { speed } \times \text { time. }$

$\begin{array}{l}{40 \mathrm{mil} / \mathrm{h} \times \mathrm{n} \text { hours }= x \text { miles }} \\\\ {\rightarrow x=40 \mathrm{n} \rightarrow(1)} \\\\ {\text { And } 60 \times(5-\mathrm{n})=260-x \text { miles }}\end{array}$

$\begin{array}{l}{\rightarrow 300-60 n=260-40 n(\text { from }(1))} \\\\ {\rightarrow 60 n-40 n=300-260} \\\\ {\rightarrow 20 n=40} \\\\ {\rightarrow n=2}\end{array}$

So, he travelled 2 hours with speed of 40 mi/h and 5 – 2 = 3 hours with speed of 60 mi/h

Hence, he travelled for 3 hours