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This pair of gears has a speed ratio of 2, or 2/1. In other words, the input gear rotates double to make the output gear turn once. Source: write my essay UK of  UK Writing Experts.

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Jeremy’s speed ——- 1u

Benjamin’s speed ——- 1u + 16

1u + 1u + 16 = 2u + 16 ——- 72/(3/4) = 96

1u ——- (96 – 16)/2 = 40

Ans : 40km/h

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Method 1: By conventional S=D/T formula

Benjamin cycled 16km/h faster.

T= 3/4 hr, D = SxT = 16 x 3/4 = 12km   

[In 3/4 hr, Benjamin would have cycled 12 km more than Jeremy].

Total distance between them is 72km, make up of Jeremy (1 unit) and Benjamin (1 unit + 12km)

So Jeremy cycled –> (72km-12km)/2units=30km     [and Benjamin cycled 30+12 = 42km]

(a) Jeremy’s speed (s) = d/T = 30/0.75 = 40km/h

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Method 2: Understanding speed and ratio

Every 1 hr, Benjamin would cycle 16km more than Jeremy.

In 3/4 hr, Benjamin would have cycled 3/4 x 16 = 12 km more than Jeremy.

Total distance between them is 72km, make up of Jeremy (1 unit) and Benjamin (1 unit + 12km)

So Jeremy cycled –> (72-12)/2=30km     [ and Benjamin cycled 30+12 = 42km]

(a) Jeremy’s speed:

            3/4 hr —–> 30km

1 hr = 4/4 hr  —-> 40km (so Jeremy’s speed is 40km/h)

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Observe their ratios… Good to understand and know.

                                               Jeremy    :  Benjamin  :  Difference  :  Total

Distance in 3/4 hr                30km     :         42km  :      12km      :   72km                        

Speed (=Distance in 1hr ) 40km/h :     56km/h  :   16km/h  :  96km/h

 

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HI SAHMOM, thank you for the detail explanation. 

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