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?

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"#

to find the time it takes (without resting).

We know:

• #"speed" = 75# #"mi/h"#

• #"distance" = 456# #"mi"#

Plugging these in:

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

#"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.