SOLUTION: Hannah travels 6 times as many minutes to work as Raoul does. Together, they travel for 63 minutes. How many minutes does Hannah travel? Draw a model and write an equation to solve

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Question 946633: Hannah travels 6 times as many minutes to work as Raoul does. Together, they travel for 63 minutes. How many minutes does Hannah travel? Draw a model and write an equation to solve.
Found 2 solutions by josmiceli, Techpriest:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = minutes that Raoul travels
+6t+ = time in minutes
------------
++t+%2B+6t+=+63+
+7t+=+63+
+t+=+9+
+6t+=+54+
Hanna travels for 54 min
-----------------------
A pie chart would work
Make 2 slices:
+%28+9%2F63+%29%2A360+ degrees
for Raoul's time
+%28+54%2F63+%29+%2A360+ degrees
for Hannah's time

Answer by Techpriest(29) About Me  (Show Source):
You can put this solution on YOUR website!
Represent Hannah as H.
Represent Raoul as R.
We can assume that Hannah is a quick woman and is able to travel 6 times as fast Raoul does, we can write it in equation form such as
+H+=+6R+
Based on the information given, we can create an equation based on how Hannah and Raoul travel together.
+H+%2B+R+=+63+
Based on the first equation given, we can use the substitution property and substitute H for R, like so the equation is now:
+6R+%2B+R+=+63+
Now we can solve the equation to find Raoul's minutes first.
+6R+%2B+R+=+63+
+7R+=+63+ Combine Like Terms
+7R%2F7+=+63%2F7+ Division Property of Equality
+R+=+9+
And since we know what R is, we know how many minutes Hannah can travel since Hannah travel 6 times as Raoul.
+H+=+6%289%29+
+H+=+54+
Now that we know how many minutes does Hannah travel, we must also show work to imply our values are correct.
+H+%2B+R+=+63+
+54+%2B+9+=+63+
+63+=+63+