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
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"#
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)
#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
