Model 1 Basic Time & Distance using formula Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (b)

Let the distance between A and B be x km, then

$x/9 - x/10 = 36/60 = 3/5$

$x/90 = 3/5$

$x = 3/5 × 90$ = 54 km.

Using Rule 9,

Here, $S_1 = 9, t_1 = x, S_2 = 10, t_2 = x - 36/60$

$S_1t_ 1 = S_2t_ 2$

$9 × x = 10(x - 36/60)$

9x = 10x - 6 = 6

Distance travelled = 9 × 6 = 54 km

Answer: (b)

90 km = 12 × 7km + 6 km.

To cover 7 km total time taken = $7/18$ hours + 6 min. = $88/3$ min.

So, (12 × 7 km) would be covered in $(12 × 88/3)$ min.

and remaining 6km is $6/18$ hrs or 20 min.

Total time = $1056/3$ + 20

= $1116/{3 × 60}$ hours = 6$1/5$ hours

= 6 hours 12 minutes.

Answer: (c)

Let the distance be x km.

Total time = 5 hours 48 minutes

= $5 + 48/60 = (5 + 4/5)$ hours

= $29/5$ hours

$x/25 + x/4 = 29/5$

${4x + 25x}/100 = 29/5$

5 × 29x = 29 × 100

$x = {29 × 100}/{5 × 29}$ = 20 km.

Here, x = 25, y = 4

Average speed = ${2xy}/{x + y}$

= ${2 × 25 × 4}/{25 + 4} = 200/29$

Total Distance = $200/29 × 5{4}/5$

= $200/29 × 29/5$ = 40 km

Required distance = 20 km

Answer: (a)

Difference of time

= 4.30 p.m - 11.a.m.

= $5{1}/2$ hours $11/2$ hours

Distance covered in $11/2$ hrs

= $5/6 - 3/8 = {20 - 9}/24 = 11/24$ part

Since, $11/24$ part of the journey is covered in $11/2$ hours

$3/8$ part of the journey is covered in

= $11/2 × 24/11 × 3/8$

= $9/2$ hours = 4$1/2$ hours.

Clearly the person started at 6.30 a.m.

Answer: (b)

Let the total journey be of x km, then

${2x}/15 + {9x}/20 + 10 = x$

$x - {2x}/15 - {9x}/20$ = 10

${60x - 8x - 27x}/60$ = 10

${25x}/60$ = 10

$x = {60 × 10}/25$ = 24 km

Answer: (b)

Using Rule 1,

Distance covered on foot

= 4 × 3$3/4$ km. = 15 km.

Time taken on cycle

= $\text"Distance"/\text"Speed" = 15/{16.5}$ hour

= ${15 × 60}/{16.5}$ minutes

= 54.55 minutes