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The table below shows the ratios of the turns of the wheels to the turns o the pedals for different gears on Nathaniel's bike. For Nathaniel to get to school on his bike, the wheels have to turn 950 times. If his bike is in gear number 3 , how many turns of the pedals are required for Nathaniel to get to school? Give your answer to 1 d.p. Gear number & turns of the wheels : turns of the pedals 1 & 1: 0.39 2 & 1: 0.31 3 & 1: 0.27 4 & 1: 0.24

Question

The table below shows the ratios of the turns of the wheels to the turns o the pedals for different gears on Nathaniel's bike. For Nathaniel to get to school on his bike, the wheels have to turn 950 times. If his bike is in gear number 3 , how many turns of the pedals are required for Nathaniel to get to school? Give your answer to 1 d.p. Gear number & turns of the wheels : turns of the pedals 1 & 1: 0.39 2 & 1: 0.31 3 & 1: 0.27 4 & 1: 0.24

The table below shows the ratios of the turns of the wheels to the turns o the pedals for different gears on Nathaniel's bike. For Nathaniel to get to school on his bike, the wheels have to turn 950 times. If his bike is in gear number 3 , how many turns of the pedals are required for Nathaniel to get to school? Give your answer to 1 d.p. Gear number & turns of the wheels : turns of the pedals 1 & 1: 0.39 2 & 1: 0.31 3 & 1: 0.27 4 & 1: 0.24

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PatrickElite · Tutor for 8 years

Answer

There will be precisely \(950 \times 0.27 = 256.5\) turns of the pedals.

Explain

## Step 1:<br />Firstly, it is crucial to understand the problem model. The ratio table mentions the relationship between the turns of the wheels (part 1 of each ratio) and turns of the pedals (part 2 of each ratio) for different gears. Here, we are given the information for gear number 3. The corresponding ratio is given in the definition field, for gear number 3, ratio \(1: 0.27\). However, there is no complete 1 turn of the wheels. Instead, there are 950 turns of the wheels.<br /><br />## Step 2:<br />Since the relationship between the turns of the wheels and the pedals for gear number 3 is given by the ratio \(1: 0.27\), when the wheels turn 950 times, the pedals would rotate equal times. To obtain the pedals' turns when the wheels turn 950 times, we need to multiply the ratio's second part (representing the turns of the pedals) with the factor representing how much the wheels turns exceed 1. <br /><br />That factor is derived by workstation of the turns of the wheels, \(950\), divided by the turns corresponding one ratio unit, \(1\) (as we compute how many times \(1\) can fit into \(950\)).<br /><br />### Formula: \((950 /1) \times 0.27 \)<br /><br />## Step 3:<br />Performing the multiplication gets the total number of turns of the pedals when there are 950 turns of the wheels and the bike is in gear number 3.
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