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Nataliya
1 month ago
11

Joshua traveled 5 hours from City A to City B. The distance between the cities is 260 miles. First he traveled at the constant s

peed 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?
Mathematics
1 answer:
Zina [12.3K]1 month ago
5 0
Joshua traveled for 3 hours at a constant speed of 60 mi/hSolution:

Notably, Joshua journeyed for a total of 5 hours between City A and City B

The distance separating both cities amounts to 260 miles.

Initially, he traveled at a consistent speed of 40 mi/h, followed by a pace of 60 mi/h.

Let us denote the hours he traveled at 40 mi/h as "n" hours which results in a distance of "x" miles

Thereafter, the time spent traveling at 60 mi/h will account for 5 – n hours and the distance covered would be 260 – x milesWe aim to discover how many hours he spent traveling at the 60 mi/h rate

The relationship connecting speed and distance is expressed 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}

Consequently, he traveled for 2 hours at a speed of 40 mi/h and for the remaining 5 – 2 = 3 hours at a speed of 60 mi/h

Thus, he traveled for 3 hours

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