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Indirect Ratios Review

Question:         How can we tell the difference between a DIRECT or INDIRECT ratio?

Answer:           We can distinguish between the two by using the 2-thumb rule.

 

Question:         What is the 2-thumb rule?

Answer:           This rule uses our own 2 thumbs.  If one thumb is pointed up and the other thumb is pointed in the same direction (up) then the ratio is DIRECT.  If one thumb is pointed up and the other thumb is pointed in the opposite direction (down) then the ratio is INDIRECT

 

The following example demonstrates how we use the thumb rule:

 

Question 1:  It takes a person 20 minutes to get home from school traveling at a velocity of 35 km/hr.  If the person increased their speed to 65 km/hr how much time will he take to go home?

 

HINT:    ALWAYS set up any ratio as if it is direct.

 

            Therefore,                      35 km/hr     x      20 minutes    

                                                65 km/hr             X minutes            

 Once we have the ratio set up as if it is DIRECT we can apply the 2-thumb rule.

Our left thumb represents the velocity (km/hr) and our right thumb represents the time (minutes).  Now we may ask ourselves the question if this is a DIRECT or INDIRECT ratio (We obtain the answer by using our thumbs)?  If the velocity increases (point left thumb upwards) will the amount of time to get home increase or decrease?  Clearly, the time to get home will decrease (because the faster we go the quicker we get somewhere), meaning our right thumb is pointed downwards.  Therefore, this question is INDIRECT because, the thumbs are pointed in opposite directions.  Since, it is INDIRECT, we flip the unknown side, cross-multiply and solve for X.

35 km/hr     x      X minutes

65 km/hr            20 minutes      

700    =     65X

700/65   =       X

10.77    =       X

Therefore, the person will reach their destination in 10.77 minutes.

 

 

 

Question 2:      If 6 liters of gasoline allows me to travel 15 kilometers.  How many kilometers can I travel with 33 liters of gasoline?

HINT:    ALWAYS set up any ratio as if it is direct. 

Therefore,                                      6 gas     x     15 km     

                                                  33 gas              X km

 

Once we have the ratio set up as if it is DIRECT we can apply the 2-thumb rule. 

Our left thumb represents the gasoline and our right thumb represents the distance (kilometers).  Now we ask ourselves the question if this question is DIRECT or INDIRECT?  We obtain the answer by using our thumbs.  If the gasoline increases (point left thumb up) does the kilometers increase or decrease? 

Obviously, the distance will also increase, meaning our right thumb is pointing up.  Therefore, this is a direct ratio.  So, we cross multiply and solve for X.

6 gas/33 gas    x     15 km/X Km 

6X      =     495

X     =     495/6

X    = 82.5

Therefore, the person can travel 82.5 kilometers with 33 liters of gasoline.

 

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