Tim buys a torch and a battery the torch costs eleven times as much as the battery Tim pays with a £10 note and get £4.86 change How much does the battery cost

The battery cost =  £0.43

Step-by-step explanation:

Tim buys a torch and a battery . The torch cost 11 times as much as the battery.  

let

cost of battery = a

cost of torch = 11a

The amount he paid is £10 note and he got a change of £4.86. That means he bought both items for 10 - 4.86 = £5.14 .

total cost = a  + 11a

5.14 = a + 11a

5.14 = 12a

divide both sides by 12

a = 5.14/12

a = 0.42833333333

a = 0.428

a ≈ 0.43

The battery cost =  £0.43

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."