A snail crawls 5/8 inch in 3/4 minute. What is the snails speed in inches per minute?

Question

Eva Abramson · Accepted Answer

#5/6# inch/minute

The necessary units will always specify which quantity is to be divided by which when working with a rate problem that compares two distinct quantities. You're interested in inches per minute in this situation. Therefore: #5/8 "inches" div 3/4 "minute"# #5/8 div 3/4# =#5/8 xx 4/3 " "larr# multiply by the reciprocal =#5/cancel8^2 xx cancel4/3# =#5/6#

Kennedy Adams · Answer

This is where the shortcut for dealing with 'divide by #3/4#' comes from.

Using the fractional format and a ratio, we get: #5/8" inches : "3/4" minutes "-> ("inches")/("minutes") = (" "5/8" ")/(3/4)# #color(brown)("But we need to change "3/4" minutes into 1 minute.")##color(brown)("We can do this by multiplying it by "4/3)# 1 can take many different forms, but when you multiply by 1, the value remains unchanged. Multiply by 1 but with #1=(" "4/3" ")/(4/3)# #color(red)([(" "5/8" ")/(3/4)color(blue)(xx" "1)] " "->" "[(" "5/8" ")/(3/4)color(blue)(xx" "(" "4/3" ")/(4/3))] # #(5/8xx4/3)/(3/4xx4/3)" " =" " (color(white)(.)5/6color(white)(.))/1 =("inches")/("minutes") # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Foot note")# You can see that it has the following if you look at the explanation's ninth line down: #5/8xx4/3# This is the shortcut part where #5/8-:3/4 -> 5/8xx4/3#

Jace Anderson · Answer

undefined To find the snail's speed in inches per minute, divide the distance traveled (5/8 inch) by the time taken (3/4 minute):

(5/8) inch ÷ (3/4) minute = (5/8) ÷ (3/4) = (5/8) × (4/3) = 20/24 inch per minute

Simplify the fraction:

20/24 inch per minute = 5/6 inch per minute

So, the snail's speed is 5/6 inch per minute.