Question #bbf57

2 Answers
Oct 16, 2017

Set up a ratio and solve for the unknown value.

Explanation:

# (6m)/(2 i) = (x m)/(10i)#

The ratio of 6 miles : 2 inches is equal to x miles /10 inches

Solve for x by multiplying both sides by 10

# 6 xx 10/2 = x xx 10/10 #

# 10/10= 1# # 10/2 =5# so

# 6 xx 5 = x#

# 60 = x #

Oct 16, 2017

#30 "miles"#

Explanation:

This is a "ratio" problem/solution. We use math to set up an expression relating the two values and units. Then, we can use that expression to evaluate other situations involving the two units. We can make a "conversion factor" by performing the division indicated by the ratio to make a single value, or use the ratio directly for a comparison, as I will in this explanation.

The "Scale" means that every actual 2 inches on the map represents an actual 6 miles on the actual land. We can write this as a ratio:

#(2"in")/(6mi)#

We could make this a conversion factor by doing the division:
#0.333 "in"/(mi)# The important think, whether a ratio or a factor, is the DIMENSIONAL ANALYSIS. That is where we make sure that the UNITS also end up in the desired dimensions.

In this case, we want to know and actual distance in miles from a map measurement of 10 inches. If we apply the factor or the ratio incorrectly, we will end up with a meaningless number.

For example, multiplying the conversion factor by the map measurement is incorrect:
#0.333 "in"/(mi) xx 10"in" = 3.33 "in"^2/(mi)# The math is correct, but the result is unusable!

We want to get miles! From our ratio and dimensional analysis we can see that we need to divide the map measurement by the ratio (or conversion factor) to get the desired units.
#10"in"/((2"in")/(6mi)) = 10"in" xx (6(mi))/(2"in")#

#5 xx 6(mi) = 30 "miles"#

For maps, the ratio method is more accurate than the approximations of some decimal conversion factors.