Question

Look at the picture and answer the following questions:

i) What is the distance from School to Library via Bus stop?
ii) What is the distance between School and Library via Hospital?
iii) Which is the shortest distance between (i) and (ii)?
iv) The distance between School and Hospital is ____________ times the distance between School and Bus stop.

Answer 1

i) Distance between school and bus stop = `3/4` km

Distance between bus stop and library = `3 1/2` km

∴ Distance between school and library = `3/4 + 3 1/2` km

= `3/4 + 7/2` km

= `3/4 + 14/4` km

= `(3 + 14)/4` km

     4
`4")"overline17`
    16
     1

= `17/4` km

= `4 1/4` km

Distance from school to library via bus stop = `4 1/4` km

ii) Distance between school and Hosptial = `4 1/2` km

Distance between Hospital and library = `1 1/4` km

∴ Distance between school and library = `4 1/2 + 1 1/4` km

= `(4 + 1/2) + (1 + 1/4)` km

= `(4 + 1) + (1/2 + 1/4)` km

= `5 + (2/4 + 1/4)` km

= `5 + 3/4` km

= `5 3/4` km

∴ Distance between school and library via Hospital = `5 3/4` km

iii) Distance of (i) [via bus stop] = `4 1/4` km

Distance of (ii) [via Hospital] = `5 3/4` km

`4 1/4 < 5 3/4`

∴ (i) is the shortest distance via bus stop

iv) Distance between school and Hospital = `4 1/2` km

Distance between school and bus stop = `3/4` km

Ratio = `4 1/2 : 3/4`

= `9/2 : 3/4`

= `18/4 : 3/4`

= 6 : 1

The distance between school and Hospital is 6 times the distance between school and bus stop.