With no stops, it takes 3 hours for a motorist to make a trip driving at an average speed of 65 mph. When the motorist stops for gas and a sandwich on the same trip, he averages 60 mph. How many minutes long is the stop?

Question

16-01-2020
Mathematics

contestada

With no stops, it takes 3 hours for a motorist to make a trip driving at an average speed of 65 mph. When the motorist stops for gas and a sandwich on the same trip, he averages 60 mph. How many minutes long is the stop?

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WaywardDelaney WaywardDelaney · Answer 1 · 2020-01-21T17:57:16+01:00

Answer:

The time for which motorist stop for gas and sandwich is 15 minutes

Step-by-step explanation:

Given as :

Let The distance cover by motorist = d miles

Let The time for which motorist stop = n minutes

The time taken by motorist to cover d distance with no stop = t = 3 hours

The average speed of motorist with no stop = s = 65 miles per hour

Again

The time taken by motorist to cover d distance with stop = T hours

The average speed of motorist with stop = S = 60 miles per hour

∵ Distance = Speed × Time

So, with no stop

d = s × t

Or, d = 65 miles per hour × 3 hours

Or, d = 195 miles

And, with stop

d = S × T

Or, d = 60 miles per hour × T hours

∵ d = 195 miles

So, 60 miles per hour × T hours = 195 miles

Or , 60 T = 195

∴ T = [tex]\dfrac{195}{60}[/tex]

i.e T = 3.25 hours

Or, T = 3 hours + [tex]\frac{25}{100}[/tex] hours

Or, T = 3 hours + [tex]\frac{1}{4}[/tex] hours

Or, T = 3 hours + [tex]\frac{60}{4}[/tex] minutes

Or, T = 3 hours + 15 minutes

So, time taken by motorist to cover d distance with stop = T = 3 h + 15 min

Now,

The time for which motorist stop = time taken by motorist to cover d distance with stop - time taken by motorist to cover d distance with no stop

i.e n = T - t

Or, n = ( 3 hours + 15 minutes) - ( 3 hours)

∴ n = 15 minutes

So, The time for which motorist stop = n = 15 minutes

Hence, The time for which motorist stop for gas and sandwich is 15 minutes . Answer