The destination of your trip is 456 miles away. How much time will you need to make the trip if you drive 75 miles per hour and take 4 rest stops that average 21 minutes each?

1 Answer
Aug 14, 2017

t_"total" = 7.5ttotal=7.5 "h"h (22 significant figures)

Explanation:

We're asked to find the time it takes to complete the journey.

What we'll be doing here is summing two different times:

  • the time it takes to travel there at a constant speed

  • the time all four rest stops took

We can use the simplified speed equation

"speed" = "distance"/"time"speed=distancetime

to find the time it takes (without resting).

We know:

  • "speed" = 75speed=75 "mi/h"mi/h

  • "distance" = 456distance=456 "mi"mi

Plugging these in:

75color(white)(l)"mi/h" = (456color(white)(l)"mi")/"time"75lmi/h=456lmitime

"time" = color(red)(ul(6.08color(white)(l)"h"

Each rest stop lasts for (an average of) 21 "min", and there are 4, so we have

4 xx 21color(white)(l)"min" = 84color(white)(l0"min"

To keep units consistent, we'll convert this to hours:

84cancel("min")((1color(white)(l)"h")/(60cancel("min"))) = color(green)(ul(1.4color(white)(l)"h"

The total time for the journey is thus

color(red)(6.08color(white)(l)"h") + color(green)(1.4color(white)(l)"h") = color(blue)(ulbar(|stackrel(" ")(" "7.5color(white)(l)"h"" ")|)

Which I'll leave at 2 significant figures.